JEE Main · 2008 · 27 Apr 2008 · Offline · Sequences and Series

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The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

(A)-4
(B)-12✓ Correct
(C)12
(D)4

Answer: (B)

Solution

Let the progression be

a, a r, a r^{2}, \dots

. The first two terms give

a (1 + r) = 12

and the next two give

a r^{2} (1 + r) = 48

; dividing the second by the first yields

r^{2} = 4

. Because the terms alternate in sign the ratio must be negative, so

r = - 2

, and then

a (1 - 2) = 12

gives

a = - 12

as the first term.

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option

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