Question

The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is

• A. 1
• B. 3
• C. 8
• D. none of these

Answer 1

The correct option is A

1

(a) 1

$a_n=128,S_n=255$ and $r=2$

$a_n=128$

$\therefore a{r}^{(n-1)}=128$

$\Rightarrow 2^{(n-1)}a=128$

$\Rightarrow \frac{2^{n}a}{2}=128$

$\Rightarrow 2^n=\frac{256}{a}$ .......... (i)

Also, $S_n=255$

$\Rightarrow a\left(\frac{r^n-1}{r-1}\right)=255$

$\Rightarrow a\left(\frac{2^n-1}{2-1}\right)=255$

$\Rightarrow a(\frac{256}{a}-1)=255$ [Using (i)]

$\Rightarrow 256-a=255$

$\Rightarrow a=256-255$

$\Rightarrow a=1$