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In a geometric sequence, the 23rd term is 16 and the 24th term is 14.  What is the 32nd term?

 Jan 2, 2024

Best Answer 

 #1
avatar+22 
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common ratio = r

first term = t

 

Because we have two consecutive terms, we know that the common difference is just the 2nd one divided by the first one. Therefore, the common difference is 14/16=7/8.

 

The 32nd term is also t(7/8)^31 and the 24th term is t(7/8)^23. Dividing, you get (7/8)^8. That means that (the 32nd term)/14=(7/8)^8. You can use a calculator to see what this is, and it is 

 

14(7/8)^8 which is about 4.81. :D

 Jan 2, 2024
 #1
avatar+22 
+1
Best Answer

common ratio = r

first term = t

 

Because we have two consecutive terms, we know that the common difference is just the 2nd one divided by the first one. Therefore, the common difference is 14/16=7/8.

 

The 32nd term is also t(7/8)^31 and the 24th term is t(7/8)^23. Dividing, you get (7/8)^8. That means that (the 32nd term)/14=(7/8)^8. You can use a calculator to see what this is, and it is 

 

14(7/8)^8 which is about 4.81. :D

yaytomath Jan 2, 2024

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