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

Algebra ->  Test -> 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      Log On


   

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) About Me  (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,

6+=+ar%5E3-ar%5E2+=+r%28ar%5E2-ar%29+=+5r
r+=+6%2F5

Then this with the given information gives us

ar%5E2-ar+=+a%2836%2F25-6%2F5%29+=+a%286%2F25%29+=+5
a+=+125%2F6

Then the first four terms are

125/6, 25, 30, 36

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