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In a geometric sequence, the 23rd term is 16 and the 26th term is 12. What is the 32nd term?

 Apr 9, 2024
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The 23rd term is equal to: \(a_1\times r^{22}\)

The 26th terms is equal to: \(a_1\times r^{25}\)

So then \(r^3= \)\(12\over{16}\)

r^3 = 3/4

r = \(\sqrt[3]{3\over4}\)

32nd term would be 23rd term times r^9

\((\sqrt[3]{3\over4})^9\)=3^3/4^3 = 27/64

16\(\times\)27/64 = 27/4

smileycoolsmiley

 Apr 10, 2024

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