SOLUTION: The second term of a geometric series is 24 and the fifth term is 3 a) show that the common ratio of the series is a half b) Find the first term of the series C) Find the

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Question 426144: The second term of a geometric series is 24 and the fifth term is 3
a) show that the common ratio of the series is a half
b) Find the first term of the series
C) Find the sum to infinity of the series
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi

The second term of a geometric series is 24 and the fifth term is 3

Geometric

a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29

a%5B2%5D+=+a%5B1%5D%2Ar+=+24  a%5B1%5D+=+24%2Fr

a[5] = (24/r)r^4 = 3 

           r^3 = 1/8

           r = 1/2   a%5B1%5D+=+48

sum%28+a%5Bn%5D%2C+n=1%2C+infinity+%29 = a%5B1%5D%2F%281-r%29 = 48/1/2 = 96