JEE Main · 2014 · 06 Apr 2014 · Offline · Sequences and Series

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Three positive numbers from an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is

(A) $2 + 3$
(B) $3 + 2$
(C) $2 - 3$
(D) $2 + 3$ ✓ Correct

Answer: (D)

Solution

Let the increasing G.P. be

a, a r, a r^{2}

. Doubling the middle term makes

a, 2 a r, a r^{2}

an A.P., so

2 (2 a r) = a + a r^{2}

, that is

4 r = 1 + r^{2}

. Then

r^{2} - 4 r + 1 = 0

gives

r = 2 \pm 3

. Since the progression increases,

r > 1

, so

r = 2 + 3

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

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