SOLUTION: For the geometric series: v1 + v2 + v3 + ... + vn it is known that: v3 - v2 = 5 and v4 - v3 = 6 Prove that the common ratio is 6/5 and find the first term. Hence find the sum o

Question 1136299: For the geometric series:
v1 + v2 + v3 + ... + vn
it is known that:
v3 - v2 = 5 and v4 - v3 = 6
Prove that the common ratio is 6/5 and find the first term. Hence find the sum of the first 4 terms of the series.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Let the first term be a and the common difference be r. Then

v2 = ar
v3 = ar^2
v4 = ar^3

Then from the given information,

Then this with the given information gives us

Then the first four terms are

125/6, 25, 30, 36

Their sum is 671/6 or 111 5/6.
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