SOLUTION: A geometric progression has first term a and common ratio r. The sum of the first three terms is 62 and the sum to infinity is 62.5. Find the value of a and the value of r.

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Question 1187276: A geometric progression has first term a and common ratio r. The sum of the first three terms is 62 and the sum to infinity is 62.5. Find the value of a and the value of r.
Answer by greenestamps(13198) About Me  (Show Source):
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Sum of first three terms: a(1+r+r^2) = 62 [1]

Infinite sum: a(1+r+r^2+...) = 62.5 [2]

Sum of terms starting with the 4th: ar^3(1+r+r^2+...) = 62.5-62 = .5 [3]

Divide [3] by [2]:

r^3 = .5/62.5 = 1/125 = (1/5)^3

r = 1/5

Substitute r=1/5 in [1] to find a:

a(1+1/5+1/25) = 62
a(1.24) = 62
a = 62/1.24 = 50

ANSWERS:
a = 50
r = 1/5