The number of terms in a G.P. is even. The sum of all its terms is thrice as large as the sum of the odd terms. The common ratio of the G.P. is

Question

The number of terms in a G.P. is even. The sum of all its terms is thrice as large as the sum of the odd terms. The common ratio of the G.P. is (A) 2 (B) 21 / n (C) (1/2) (D) √2

Tardigrade Admin · Accepted Answer

(a(r2 n-1)/r-1)=3 (a(r2 n-1)/r2-1) ; (3/r+1)=1 ⇒ r=2 ⇒(A)

Q. The number of terms in a G.P. is even. The sum of all its terms is thrice as large as the sum of the odd terms. The common ratio of the G.P. is

2

$2^{1/ n}$

$\frac{1}{2}$

$2$

$\frac{a ( r ^{2 n} - 1 )}{r - 1} = 3 \frac{a ( r ^{2 n} - 1 )}{r ^{2} - 1}; \frac{3}{r + 1} = 1 \Rightarrow r = 2 \Rightarrow (A)$

Q. The number of terms in a G.P. is even. The sum of all its terms is thrice as large as the sum of the odd terms. The common ratio of the G.P. is

2

21/n

21​

2​

r−1a(r2n−1)​=3r2−1a(r2n−1)​;r+13​=1⇒r=2⇒(A)

$2^{1/ n}$

$\frac{1}{2}$

$2$

$\frac{a ( r ^{2 n} - 1 )}{r - 1} = 3 \frac{a ( r ^{2 n} - 1 )}{r ^{2} - 1}; \frac{3}{r + 1} = 1 \Rightarrow r = 2 \Rightarrow (A)$