Explanation
<ul><li>2 to 9: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mn>3</mn></msup><mo>+</mo><mn>1</mn><mo>=</mo></mrow></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">9</span></span></span></span></li><li>9 to 28: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>3</mn><mn>3</mn></msup><mo>+</mo><mn>1</mn><mo>=</mo></mrow></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">28</span></span></span></span></li><li>28 to 65: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>4</mn><mn>3</mn></msup><mo>+</mo><mn>1</mn><mo>=</mo></mrow></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">65</span></span></span></span></li><li>65 to 126: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>5</mn><mn>3</mn></msup><mo>+</mo><mn>1</mn><mo>=</mo></mrow></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">126</span></span></span></span></li><li>126 to 217: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>6</mn><mn>3</mn></msup><mo>+</mo><mn>1</mn><mo>=</mo></mrow></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="mord">217</span></span></span></span></li></ul><p>The pattern seems to be <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">n^3 + 1</annotation></semantics></math></span></span>, where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut"></span><span class="mord mathnormal">n</span></span></span></span> is the position of the term in the sequence (starting from 1).</p><p>Now, let`s find the next term using <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>7</mn><mn>3</mn></msup><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">7^3 + 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut"></span><span class="mord"><span class="mord">7</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span><span class="mspace"></span><span class="mbin">+</span><span class="mspace"></span></span><span class="base"><span class="strut"></span><span class="mord">1</span></span></span></span>:</p><ul><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>7</mn><mn>3</mn></msup><mo>+</mo><mn>1</mn><mo>=</mo><mn>343</mn><mo>+</mo><mn>1</mn><mo>=</mo><mn>344</mn></mrow><annotation encoding="application/x-tex">7^3 + 1 = 343 + 1 = 344</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut"></span><span class="mord"><span class="mord">7</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span><span class="mspace"></span><span class="mbin">+</span><span class="mspace"></span></span><span class="base"><span class="strut"></span><span class="mord">1</span><span class="mspace"></span><span class="mrel">=</span><span class="mspace"></span></span><span class="base"><span class="strut"></span><span class="mord">343</span><span class="mspace"></span><span class="mbin">+</span><span class="mspace"></span></span><span class="base"><span class="strut"></span><span class="mord">1</span><span class="mspace"></span><span class="mrel">=</span><span class="mspace"></span></span><span class="base"><span class="strut"></span><span class="mord">344</span></span></span></span></li></ul><p>Therefore, the next term in the sequence should be <strong>344</strong>.</p>
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