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The 23rd term in a certain geometric sequence is 16 and the 28th term in the sequence is 24. What is the 43rd term?

 Aug 4, 2020
 #1
avatar+169 
+2

Well, try to find the difference. We have 5 terms from 16 to 24, and the difference is 8. so, each step must be increasing by 8/5. This gives the order:

 

\(23rd: 16\\ 24th: 16\frac{8}{5}\\ 25th: 16\frac{8\cdot2}{5}\\ 26th: 16\frac{8\cdot3}{5}\\\)

We have a pattern, and that is that the answer for a given sequence is for any term \(n\), we have \(16+\frac{8*(n-23)}{5}\). Try numbers out! And most importantly, plug 43 into that expression. What do you get?

 Aug 4, 2020
edited by Inspirational  Aug 4, 2020
 #2
avatar+26767 
+1

multiply  r^5   x 16   to get to 24

      24 =  16 r^5        r = \(\sqrt[5]{24/16}\)

 

\(\sqrt[5]{24/16}\) )20  * 16 = 81

 Aug 4, 2020

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