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avatar+117 

How many terms are there in a geometric series if the first term is 3, the common ratio is 2, and the sum of the series is 93?

Hint: r ≠ 1, where a1 is the first term and r is the common ratio.

 n = 3

 n = 4

 n = 5

 n = 6

 

I know it's not D...could you help me please?

failurewithasmile  Apr 14, 2017
 #1
avatar+87301 
+2

We have that

 

S  = first term ( 1 - r^n) / (1 - r)  ......so.....

 

93   =  3  (1 - 2^n) ( 1 - 2)         divide both sides by 3

 

31  = (1- 2^n) / -1      multiply both sides by -1

 

-31  =  (1 - 2^n)        multiply both sides by -1 again

 

31  =  2^n  - 1      add 1 to both sides

 

32  = 2^n         →    n  = 5   terms

 

 

 

cool cool cool

CPhill  Apr 14, 2017

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