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<title>Arithmetic sequences 1</title>
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<div class="exercise">
<div class="problems">
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<div class="vars">
<var id="A">randRange(-10, 10)</var>
<var id="D">randRangeNonZero(-6, 6)</var>
<var id="N">randRange(3, 5)</var>
<var id="GIVEN">_.map(_.range(N), function(i) { return A + i * D; })</var>
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<div class="question">
<p>The first <var>cardinalThrough20(N)</var> terms of an arithmetic sequence are given:</p>
<p><code><var>GIVEN.join(",")</var>, \ldots</code></p>
<p class="question">What is the <var>ordinalThrough20(N + 1)</var> term in the sequence?</p>
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<div class="solution" data-forms="integer"><var>A + D * N</var></div>
<div class="hints">
<p>In any arithmetic sequence, each term is equal to the previous term plus the common difference.</p>
<p data-if="D > 0">Thus, the second term is equal to the first term plus the common difference. In this sequence, the second term, <code><var>A + D</var></code>, is <code><var>abs(D)</var></code> more than the first term, <code><var>A</var></code>.</p><p data-else="">Thus, the second term is equal to the first term plus the common difference. In this sequence, the second term, <code><var>A + D</var></code>, is <code><var>abs(D)</var></code> less than the first term, <code><var>A</var></code>.</p>
<p>Therefore, the common difference is <code><var>D</var></code>.</p>
<p>The <var>ordinalThrough20(N + 1)</var> term in the sequence is equal to the <var>ordinalThrough20(N)</var> term plus the common difference, or <code><var>A + D * (N - 1)</var> + <var>D</var> = <var>A + D * N</var></code>.</p>
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