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The sum of the first terms n in the infinite geometric sequence {1/4, 1/8, 1/16, ..} is 15/32. Find n.

 Dec 27, 2021
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The formula for the sum of a finite geometric series is:  Sum  =  [ a · ( 1 - rn ) ] / (1 - r)

 

For this problem, the first term  a = 1/4.

For this problem, the common ratio  r = 1/2.

 

So:  15/32  =   [ ¼ · ( 1 - ½n ) ] / (1 - ½)

        15/32  =   [ ¼ · ( 1 - ½n ) ] / (½)

        15/32  =  ½ · ( 1 - ½n )

        15/16  =  1 - ½n

         -1/16  =  - ½n 

           1/16  =  ½n 

                n  =  4

 Dec 27, 2021

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