The 5th and 8th terms of a G.P. are 1458 and 54 respectively. The common ratio of the G.P. is

Question

The 5th and 8th terms of a G.P. are 1458 and 54 respectively. The common ratio of the G.P. is (A) (1/3) (B) 3 (C) 9 (D) (1/9)

Tardigrade Admin · Accepted Answer

Let a and r be the first term and common ratio of the GP. It is given that, a5=1458 and a8=54 ⇒ a r4=1458 and a r7=54 ⇒ (a r7/a r4)=(54/1458) ⇒ r3=(1/27) ⇒ r =(1/3)

Q. The $5^{t} h$ and $8^{t h}$ terms of a $G . P .$ are $1458$ and $54$ respectively. The common ratio of the $G . P .$ is

$\frac{1}{3}$

3

9

$\frac{1}{9}$

$\frac{1}{8}$

Let $a$ and $r$ be the first term and common ratio of the GP. It is given that,
$a_{5} = 1458$ and $a_{8} = 54$
$\Rightarrow a r^{4} = 1458$ and $a r^{7} = 54$
$\Rightarrow \frac{a r ^{7}}{a r ^{4}} = \frac{54}{1458}$
$\Rightarrow r^{3} = \frac{1}{27}$
$\Rightarrow r = \frac{1}{3}$

Q. The 5th and 8th terms of a G.P. are 1458 and 54 respectively. The common ratio of the G.P. is

31​

3

9

91​

81​

Let a and r be the first term and common ratio of the GP. It is given that, a5​=1458 and a8​=54 ⇒ar4=1458 and ar7=54 ⇒ar4ar7​=145854​ ⇒r3=271​ ⇒r=31​

Q. The $5^{t} h$ and $8^{t h}$ terms of a $G . P .$ are $1458$ and $54$ respectively. The common ratio of the $G . P .$ is

$\frac{1}{3}$

$\frac{1}{9}$

$\frac{1}{8}$

Let $a$ and $r$ be the first term and common ratio of the GP. It is given that,
$a_{5} = 1458$ and $a_{8} = 54$
$\Rightarrow a r^{4} = 1458$ and $a r^{7} = 54$
$\Rightarrow \frac{a r ^{7}}{a r ^{4}} = \frac{54}{1458}$
$\Rightarrow r^{3} = \frac{1}{27}$
$\Rightarrow r = \frac{1}{3}$