Question

If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. 2
• D. 4

Answer 1

The correct option is D

4

(d) 4

$a_2=2$

$\therefore ar=2$ ...... (i)

Also, $S_{infty=8}$

$\Rightarrow \frac{a}{(1-r)}=8$

$\Rightarrow \frac{a}{(1-\frac{2}{a})}=8$ [Using (i)]

$\Rightarrow a^2=8(a-2)$

$\Rightarrow a^2-8a+16=0$

$\Rightarrow (a-4{)}^2=0$

$\Rightarrow a=4$