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JEE Main 2016 Paper

Section: Mathematics

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Question : 32 of 90

Marks: +1, -0

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

$\frac{4}{3}$
1
$\frac{7}{4}$
$\frac{8}{5}$

Solution:

Let the G.P. be

a, ar, ar^2

and termss of A.P are A + d, A + 4d , A + 8d

then

\frac{ar^2-ar}{ar-a}=\frac{(A+8d)-(A+4d)}{(A+4d)-(A+8d)}=\frac{4}{3}

\Rightarrow r=\frac{4}{3}

Alternate Solution:

Let Ap is a,a + d,a + 2d

2nd,5th and 9th terms a + d,a + 4d,a + 8d are in G.P

\Rightarrow (a+4d)^2=(a+d)(a+8d)

\Rightarrow d(8d-a)=0\Rightarrow 8d=a

as

d \neq 0

Hence common ratio of GP

\frac{a+4d}{a+d}=\frac{8d+4d}{8d+d}=\frac{12d}{9d}=\frac{4}{3}

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