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Let a, b and c be the 7th, 11th and 13th...

Let a, b and c be the 7th, 11th and 13th terms, respectively, of a non-constant A.P.. If these are also the three consecutive terms of a G.P., then `(a)/(c )` is equal to

A

`1/2`

B

`2`

C

`4`

D

`7/13`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the first term of the A.P be a and common difference be d.
Let the first term of the G.P be A and common ratio be r.
`a=a+6d=A`
`b=a+10d=Ar`
`c=a+12d=Ar^(2)`
`A(r-1)=4d, Ar(r-1)=2d`
`rArr" "r=(1)/(2)" "rArr" "(a)/(c)=(1)/(r^(2))=4`
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