# arithmetic

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How do i find the common ratio, when the 1st, 2nd and 7th terms of a A.P with common difference 2 are the first three terms of a G.P .

• arithmetic -

The first, second, and seventh terms of your AP would be
a, a+2, and a+12

but these are supposed to be the first 3 terms of a GP, so
(x+2)/a = (a+12)/(a+2)
cross-multiply, the a^2 drops out and you get
a = 1/2

now you know your first 3 terms of the GP to be
1/2, 5/2, and 25/2

check for common ratio:
(5/2) ÷ (1/2) = 5
(25/2) ÷ (5/2) = 5

• Correction - Typo in arithmetic -

(x+2)/a = (a+12)/(a+2)

obviously should have been

(a+2)/a = (a+12)/(a+2)

• arithmetic -

Hey thanks a lot Reiny. I got it..

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