Interactive Demo: Arithmetic Sequence General Term and Sum Formulas
2020-03-11 12:00
This GeoGebra applet dynamically demonstrates the core formulas of arithmetic sequences: the general term formula aₙ = a₁ + (n-1)d and the sum of the first n terms Sₙ = na₁ + n(n-1)d/2. Interactive sliders allow real-time adjustment of the first term a₁, common difference d, and number of terms n, enabling observation of how sequence terms and their sum change. The Sequence command generates terms
In collections
Secondary Vocational Mathematics
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.574.0" app="classic" platform="w" id="2afede64-497b-4233-878d-db6e7db31ef3" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1350" height="560" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.9985185185185185" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3" size="1348" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="221" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="145" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="243" window="100,100,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1347" height="557"/>
<coordSystem xZero="140.64057839685123" yZero="214.06723601162923" scale="28.34863511815054" yscale="28.34863882614912"/>
<evSettings axes="false" grid="true" gridIsBold="false" pointCapturing="2" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="224" g="224" b="224"/>
<lineStyle axes="1" grid="20"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1" tickExpression="1"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1" tickExpression="1"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="0"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<command name="Point">
<input a0="Segment[(-3, -1), (-3, -15)]"/>
<output a0="N"/>
</command>
<element type="point" label="N">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-36" y="26"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-3" y="-8" z="1"/>
<pointSize val="7"/>
<pointStyle val="1"/>
<caption val="$\Large n$"/>
</element>
<command name="Point">
<input a0="Segment[(1, 2), (10, 2)]"/>
<output a0="A_1"/>
</command>
<element type="point" label="A_1">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-9" y="6"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4" y="2" z="1"/>
<pointSize val="7"/>
<pointStyle val="1"/>
<caption val="$\Large a_1$"/>
</element>
<command name="Point">
<input a0="Segment[(x(A_1), 1), (x(A_1) + 5, 1)]"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="7" y="1" z="1"/>
<pointSize val="7"/>
<pointStyle val="1"/>
<caption val="$\Large d$"/>
</element>
<expression label="n" exp="abs(y(N))" />
<element type="numeric" label="n">
<value val="8"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="a_1" exp="x(A_1)" />
<element type="numeric" label="a_1">
<value val="4"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="d" exp="x(D) - x(A_1)" />
<element type="numeric" label="d">
<value val="3"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Vector">
<input a0="N" a1="(-3, 0)"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0" y="8" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="N"/>
</element>
<command name="Vector">
<input a0="(-3, 0)" a1="N"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="0" y="-8" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="-3" y="0" z="1"/>
</element>
<command name="Sequence">
<input a0="Sequence[Polygon[(i, (-k)), (i + 1, (-k)), 4], i, 0, a_1 - 1]" a1="k" a2="1" a3="n"/>
<output a0="l2"/>
</command>
<element type="list" label="l2">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Sequence[Polygon[(i - 1, (-k)), (i, (-k)), 4], i, a_1 + 1, a_1 + ((k - 1) * d)]" a1="k" a2="2" a3="n"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<show object="true" label="true" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Vector">
<input a0="(a_1, (-n) - 1)" a1="(a_1 + ((n - 1) * d), (-n) - 1)"/>
<output a0="e"/>
</command>
<element type="vector" label="e">
<show object="true" label="false" ev="4"/>
<condition showObject="gc > 2"/>
<objColor r="128" g="0" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="21" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="4" y="-9" z="1"/>
</element>
<command name="Vector">
<input a0="(a_1 + ((n - 1) * d), (-n) - 1)" a1="(a_1, (-n) - 1)"/>
<output a0="f"/>
</command>
<element type="vector" label="f">
<show object="true" label="false" ev="4"/>
<condition showObject="gc > 2"/>
<objColor r="128" g="0" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-21" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="25" y="-9" z="1"/>
</element>
<command name="Vector">
<input a0="(0, (-n) - 1)" a1="(a_1, (-n) - 1)"/>
<output a0="g"/>
</command>
<element type="vector" label="g">
<show object="true" label="false" ev="4"/>
<condition showObject="gc > 1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="4" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="0" y="-9" z="1"/>
</element>
<command name="Vector">
<input a0="(a_1, (-n) - 1)" a1="(0, (-n) - 1)"/>
<output a0="h"/>
</command>
<element type="vector" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="gc > 1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-4" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="4" y="-9" z="1"/>
</element>
<command name="Vector">
<input a0="(0, (-n) - 2)" a1="(a_1 + ((n - 1) * d), (-n) - 2)"/>
<output a0="i"/>
</command>
<element type="vector" label="i">
<show object="true" label="false" ev="4"/>
<condition showObject="gc > 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="25" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="0" y="-10" z="1"/>
</element>
<command name="Vector">
<input a0="(a_1 + ((n - 1) * d), (-n) - 2)" a1="(0, (-n) - 2)"/>
<output a0="j"/>
</command>
<element type="vector" label="j">
<show object="true" label="false" ev="4"/>
<condition showObject="gc > 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-25" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="25" y="-10" z="1"/>
</element>
<command name="Vector">
<input a0="(0, 2)" a1="A_1"/>
<output a0="w"/>
</command>
<element type="vector" label="w">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="4" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="0" y="2" z="1"/>
</element>
<command name="Vector">
<input a0="A_1" a1="(0, 2)"/>
<output a0="a"/>
</command>
<element type="vector" label="a">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-4" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="A_1"/>
</element>
<command name="Vector">
<input a0="(a_1, 1)" a1="D"/>
<output a0="b"/>
</command>
<element type="vector" label="b">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="3" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="4" y="1" z="1"/>
</element>
<command name="Vector">
<input a0="D" a1="(a_1, 1)"/>
<output a0="c"/>
</command>
<element type="vector" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-3" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="D"/>
</element>
<command name="Midpoint">
<input a0="(a_1, 0)" a1="(a_1 + ((n - 1) * d), (-n))"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="14.5" y="-4" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="angle" label="α">
<angleStyle val="3"/>
<value val="0"/>
<slider min="0" max="180°" absoluteScreenLocation="true" width="180" x="68" y="48" fixed="false" horizontal="true" showAlgebra="true"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="10" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
<animation speed="1" type="0" playing="false"/>
</element>
<command name="Rotate">
<input a0="l2" a1="(-α)" a2="C"/>
<output a0="l2'"/>
</command>
<element type="list" label="l2'">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Rotate">
<input a0="l1" a1="(-α)" a2="C"/>
<output a0="l1'"/>
</command>
<element type="list" label="l1'">
<show object="true" label="true" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Vector">
<input a0="(a_1 + ((n - 1) * d), (-n) - 1)" a1="((2 * a_1) + ((n - 1) * d), (-n) - 1)"/>
<output a0="k"/>
</command>
<element type="vector" label="k">
<show object="false" label="false" ev="4"/>
<condition showObject="α ≟ 180° ∧ gc > 4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="4" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="25" y="-9" z="1"/>
</element>
<command name="Vector">
<input a0="((2 * a_1) + ((n - 1) * d), (-n) - 1)" a1="(a_1 + ((n - 1) * d), (-n) - 1)"/>
<output a0="l"/>
</command>
<element type="vector" label="l">
<show object="false" label="false" ev="4"/>
<condition showObject="α ≟ 180° ∧ gc > 4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-4" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="29" y="-9" z="1"/>
</element>
<command name="Vector">
<input a0="(a_1 + ((n - 1) * d), (-n) - 2)" a1="((2 * a_1) + ((n - 1) * d), (-n) - 2)"/>
<output a0="m"/>
</command>
<element type="vector" label="m">
<show object="true" label="false" ev="4"/>
<condition showObject="α ≟ 180° ∧ gc > 4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="4" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="25" y="-10" z="1"/>
</element>
<command name="Vector">
<input a0="((2 * a_1) + ((n - 1) * d), (-n) - 2)" a1="(a_1 + ((n - 1) * d), (-n) - 2)"/>
<output a0="p"/>
</command>
<element type="vector" label="p">
<show object="true" label="false" ev="4"/>
<condition showObject="α ≟ 180° ∧ gc > 4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-4" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="29" y="-10" z="1"/>
</element>
<command name="Sequence">
<input a0="Text[((("a_" * i) * "=") * LaTeX[a_1 + ((i - 1) * d)]), (-2, (-i) + 0.4)]" a1="i" a2="1" a3="n"/>
<output a0="l3"/>
</command>
<element type="list" label="l3">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<font serif="true" sizeM="1.4" size="5" style="2"/>
<angleStyle val="0"/>
</element>
<command name="Vector">
<input a0="(0, (-n) - 3)" a1="((2 * a_1) + ((n - 1) * d), (-n) - 3)"/>
<output a0="q"/>
</command>
<element type="vector" label="q">
<show object="true" label="false" ev="4"/>
<condition showObject="α ≟ 180° ∧ gc > 5"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="29" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="0" y="-11" z="1"/>
</element>
<command name="Vector">
<input a0="((2 * a_1) + ((n - 1) * d), (-n) - 3)" a1="(0, (-n) - 3)"/>
<output a0="r"/>
</command>
<element type="vector" label="r">
<show object="true" label="false" ev="4"/>
<condition showObject="α ≟ 180° ∧ gc > 5"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-29" y="0" z="0"/>
<lineStyle thickness="1" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint x="29" y="-11" z="1"/>
</element>
<expression label="text7" exp=""s_n=\frac{(a_1+a_n)n}{2}""/>
<element type="text" label="text7">
<show object="true" label="true" ev="40"/>
<condition showObject="α ≟ 180° ∧ gc > 6"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="5" style="1"/>
<absoluteScreenLocation x="427" y="75"/>
</element>
<expression label="text8" exp=""s_n=\frac{[2a_1+(n-1)d]n}{2}\\=na_1+\frac{n(n-1)}{2}d""/>
<element type="text" label="text8">
<show object="true" label="true" ev="40"/>
<condition showObject="α ≟ 180° ∧ gc > 8"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="5" style="1"/>
<absoluteScreenLocation x="626" y="75"/>
</element>
<command name="Text">
<input a0=""a_1+a_n"" a1="(a_1 + ((n - 1) * d / 2) - 3, (-n) - 3.6)"/>
<output a0="text6"/>
</command>
<element type="text" label="text6">
<show object="true" label="true" ev="8"/>
<condition showObject="α ≟ 180° ∧ gc > 5"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="5" style="2"/>
<startPoint x="11.5" y="-11.6" z="1"/>
</element>
<command name="Text">
<input a0=""2a_1+(n-1)d"" a1="(a_1 + ((n - 1) * d / 2) + 1, (-n) - 3.6)"/>
<output a0="text9"/>
</command>
<element type="text" label="text9">
<show object="true" label="true" ev="8"/>
<condition showObject="α ≟ 180° ∧ gc > 7"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="5" style="2"/>
<startPoint x="15.5" y="-11.6" z="1"/>
</element>
<element type="numeric" label="gc">
<value val="1"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-11" y="3"/>
<labelMode val="3"/>
<slider min="1" max="9" absoluteScreenLocation="true" width="180" x="68" y="100" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<caption val="$步骤%v$"/>
</element>
<command name="Text">
<input a0=""a_1"" a1="(a_1 / 2, (-n) - 1.5)"/>
<output a0="text1"/>
</command>
<element type="text" label="text1">
<show object="true" label="true" ev="8"/>
<condition showObject="gc > 1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="5" style="2"/>
<startPoint x="2" y="-9.5" z="1"/>
</element>
<command name="Text">
<input a0=""(n-1)d"" a1="(a_1 + ((n - 1) * d / 2) - 2, (-n) - 1.6)"/>
<output a0="text2"/>
</command>
<element type="text" label="text2">
<show object="true" label="true" ev="8"/>
<condition showObject="gc > 2"/>
<objColor r="128" g="0" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="5" style="2"/>
<startPoint x="12.5" y="-9.6" z="1"/>
</element>
<command name="Text">
<input a0=""a_1"" a1="((3 * a_1 / 2) + ((n - 1) * d), (-n) - 1.5)"/>
<output a0="text4"/>
</command>
<element type="text" label="text4">
<show object="true" label="true" ev="8"/>
<condition showObject="α ≟ 180° ∧ gc > 4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="5" style="2"/>
<startPoint x="27" y="-9.5" z="1"/>
</element>
<command name="Text">
<input a0=""a_n=a_1+(n-1)d"" a1="((a_1 + ((n - 1) * d)) / 2 - 2, (-n) - 2.6)"/>
<output a0="text3"/>
</command>
<element type="text" label="text3">
<show object="true" label="true" ev="8"/>
<condition showObject="gc > 3"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="5" style="2"/>
<startPoint x="10.5" y="-10.6" z="1"/>
</element>
<command name="Text">
<input a0=""a_1"" a1="((3 * a_1 / 2) + ((n - 1) * d), (-n) - 2.5)"/>
<output a0="text5"/>
</command>
<element type="text" label="text5">
<show object="true" label="true" ev="8"/>
<condition showObject="α ≟ 180° ∧ gc > 4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="5" style="2"/>
<startPoint x="27" y="-10.5" z="1"/>
</element>
<expression label="text10" exp=""等差数列的通项公式、前n项和公式""/>
<element type="text" label="text10">
<show object="true" label="true" ev="40"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<bgColor r="255" g="127" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="12" style="1"/>
<absoluteScreenLocation x="376" y="15"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="273" y="75"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(gc,gc+1)"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<caption val="next"/>
</element>
</construction>
</geogebra>