If the term of an infinite G.P. is equal to twice the sum of all the terms that follows it, then the common ratio is

Question

If the term of an infinite G.P. is equal to twice the sum of all the terms that follows it, then the common ratio is (A) 2 (B) 1 (C)  (1 /2) (D)  (1 /3)

Tardigrade Admin · Accepted Answer

By the given condition a= 2[ar+ar2+ar3+.......] ∴ a= 2 (ar/1-r) ⇒ 1= (2r/1-r) ⇒ 1-r = 2r ⇒ 3r= 1 ⇒ r= (1/3) .

Q. If the term of an infinite G.P. is equal to twice the sum of all the terms that follows it, then the common ratio is

2

1

$\frac{1}{2}$

$\frac{1}{3}$

By the given condition
$a = 2 [a r + a r^{2} + a r^{3} + .......]$
$∴ a = 2 \frac{a r}{1 - r}$
$\Rightarrow 1 = \frac{2 r}{1 - r}$
$\Rightarrow 1 - r = 2 r$
$\Rightarrow 3 r = 1$
$\Rightarrow r = \frac{1}{3}$ .

Q. If the term of an infinite G.P. is equal to twice the sum of all the terms that follows it, then the common ratio is

2

1

21​

31​

By the given condition a=2[ar+ar2+ar3+.......] ∴a=21−rar​ ⇒1=1−r2r​ ⇒1−r=2r ⇒3r=1 ⇒r=31​ .

$\frac{1}{2}$

$\frac{1}{3}$

By the given condition
$a = 2 [a r + a r^{2} + a r^{3} + .......]$
$∴ a = 2 \frac{a r}{1 - r}$
$\Rightarrow 1 = \frac{2 r}{1 - r}$
$\Rightarrow 1 - r = 2 r$
$\Rightarrow 3 r = 1$
$\Rightarrow r = \frac{1}{3}$ .