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

omgitsrne Feb 22, 2024

#1**+1 **

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.__

hairyberry Feb 22, 2024