SOLUTION: The 2nd , 4th , and 7th terms of an AP are the first 3 consecutive terms of a GP . Find : a) the common difference b) the sum of the frst eight terms of the GP if the common differ

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Question 1175729: The 2nd , 4th , and 7th terms of an AP are the first 3 consecutive terms of a GP . Find : a) the common difference b) the sum of the frst eight terms of the GP if the common difference of the AP is 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a)
In the AP:
T%5B2%5D+=+a%2Bd, T%5B4%5D+=a%2B3d,T%5B7%5D+=+a%2B6d
In the GP: %28a%2Bd%29%28a%2B6d%29+=+%28a%2B3d%29%5E2, or
a%5E2%2B7ad%2B6d%5E2+=+a%5E2%2B6ad%2B9d%5E2, or
ad+=+3d%5E2, or
a+=+3d
if given a+=+2, then highlight%28d+=+2%2F3%29

The common ratio of the GP is highlight%28r=+3%2F2%29=> Answer.

Check:
%282+%2B+2%2F3%29, %282+%2B+3%2A2%2F3%29, %282+%2B+6%2A2%2F3%29
= 8%2F3, 4, 6

Common ratio: 4%2F%288%2F3%29+=+3%2F2 same as 6%2F4+=+3%2F2=>confirmed

b) the sum of the first eight terms of the GP
a%2Bar%2Bar%5E2%2Bar%5E3%2Bar%5E4%2Bar%5E5%2Bar%5E6%2Bar%5E7....if a+=+2 and +r=3%2F2
=
=6305%2F64
=98.515625