<p>The first three terms of an infinite series are ${16,x,9}$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the value(s) of $x$, if the series is</div><ol class="abc-list"><li><div class="list-item-paragraph">geometric,</div></li><li><div class="list-item-paragraph">arithmetic.<span class="inline-marks">[3]</span></div></li></ol></li><li><div class="list-item-paragraph">If all the terms in part <strong>(i)(a)</strong> are positive, calculate its sum to infinity.<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Given that the sum of the first $n$ terms in part <strong>(i)(b)</strong> is less than $-64$, find the least value of $n$.<span class="inline-marks">[3]</span></div></li></ol>

The first three terms of an infinite series are ${16,x,9}$.

Find the value(s) of $x$, if the series is

If all the terms in part (i)(a) are positive, calculate its sum to infinity.

If all the terms in part **(i)(a)** are positive, calculate its sum to infinity.

Given that the sum of the first $n$ terms in part (i)(b) is less than $-64$, find the least value of $n$.

Given that the sum of the first $n$ terms in part **(i)(b)** is less than $-64$, find the least value of $n$.

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