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If the 2nd, 5th and 19th terms of a non-...

If the 2nd, 5th and 19th terms of a non-constant AP are in GP, then the common ratio of this GP is

A

`(8)/(5)`

B

`(4)/(3)`

C

1

D

`(7)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let a be the first term and d be the common difference.
Then, we have `a + d, a + 4d, a + 8d` in GP,
i.e `(a + 4d)^(2) = (a + d) (a + 8d)`
`rArr a^(2) + 16d^(2) + 8ad = a^(2) + 8ad + ad + 8d^(2)`
`rArr 8d^(2) = ad`
`rArr 8d = a " " [ :' d != 0]`
Now, common ratio,
`r = (a + 4d)/(a + d) = (8d + 4d)/(8d + d) = (12d)/(9d) = (4)/(3)`
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