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Consider the geometric sequence 125/9, 25, 45, .... What is the eighth term of the sequence? Express your answer as a common fraction.

 Dec 14, 2021
 #1
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45 / 25 ==9 / 5 - this is the common ratio.

 

Your GS looks like this:

 

125 / 9 , 25 , 45 , 81 , 729 / 5 , 6561 / 25 , 59049 / 125 , 531441 / 625 , 4782969 / 3125 , 43046721 / 15625 , >>Number of terms = 10>>Total Sum == 869254694 / 140625

 

The 8th term==531441 / 625

 Dec 14, 2021
 #2
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Sequence: 125/9, 25, 45, ...

a=125/9, r = 25/(125/9) = 225/125 = 9/5, Gen Term= ar^(n-1) 

8th term = (125/9)(9/5)^7 = (125/9)(4782969/78125) = 531 441/ 625

 Dec 14, 2021

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