JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Sequences and Series

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If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is :

(A)760
(B)755
(C)750
(D)757✓ Correct

Answer: (D)

Solution

Let the first term be

a

and ratio

r > 0

. Then

a r (1 + r^{2} + r^{4}) = 21

and

a r^{7} (1 + r^{2} + r^{4}) = 15309

. Dividing,

r^{6} = \frac{15309}{21} = 729

, so

r = 3

. Substituting,

a \cdot 3 \cdot 91 = 21

, giving

a = \frac{1}{13}

. The sum of the first nine terms is

S_{9} = \frac{a ( r ^{9} - 1 )}{r - 1} = \frac{\frac{1}{13} ( 19683 - 1 )}{2} = \frac{19682}{26} = 757

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Single correct option

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