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In a geometric sequence, the 23rd term is 16 and the 24th term is 1/4.  What is the 30th term?

 Feb 22, 2024
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The common difference between terms is \(\frac{\frac{1}{4}}{16}=\frac{1}{64}\).

The 30th term is 30-24=6 terms away, meaning 6 common differences from 24.

So, the 30th term is \(\frac{1}{4}*{(\frac{1}{64})}^6\)\(\frac{1}{{2}^{2}}*\frac{1}{{2}^{36}}=\frac{1}{{2}^{38}}\), is our final answer.

 Feb 22, 2024

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