The ratio of sum of first three terms of a G.P. to the sum of first six terms is 64: 91, the common ratio of GP. is

Question

The ratio of sum of first three terms of a G.P. to the sum of first six terms is 64: 91, the common ratio of GP. is (A) (1/4) (B) (3/4) (C) (5/4) (D) (7/4)

Tardigrade Admin · Accepted Answer

Given, (S3/S6) = (64/91) = (a (r3 - 1)/a (r6 - 1)) ⇒ ((r3 -1 )/(r3 + 1) (r3 - 1)) = (64/91) ⇒ r3 = (27/64) ∴ r = (3/4)

Q. The ratio of sum of first three terms of a $G . P$ . to the sum of first six terms is $64 : 91$ , the common ratio of $GP$ . is

$\frac{1}{4}$

$\frac{3}{4}$

$\frac{5}{4}$

$\frac{7}{4}$

Given, $\frac{S _{3}}{S _{6}} = \frac{64}{91} = \frac{a ( r ^{3} - 1 )}{a ( r ^{6} - 1 )}$
$\Rightarrow \frac{( r ^{3} - 1 )}{( r ^{3} + 1 ) ( r ^{3} - 1 )} = \frac{64}{91}$
$\Rightarrow r^{3} = \frac{27}{64} ∴ r = \frac{3}{4}$

Q. The ratio of sum of first three terms of a G.P. to the sum of first six terms is 64:91, the common ratio of GP. is

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