Question

If the sum of $n$ terms of a G.P. is 255 and $n ^ { t h }$ terms is 128 and common ratio is 2, then first term will be.

• A. 1
• B. 3
• C. 7
• D. None of these

Answer 1

Answer: (A)

1

Answer 2

Given that $\frac { a \left( r ^ { n } - 1 \right) } { r - 1 } = 255$ $( \because r > 1 )$ …..(i)

$a r ^ { n - 1 } = 128$ …..(ii)

and common ratio $r = 2$ …..(iii)

From (iii), (i) and (ii)

we get …..(iv)

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

Dividing (v) by (iv)

we get $\frac { 2 ^ { n } - 1 } { 2 ^ { n - 1 } } = \frac { 255 } { 128 }$ $\Rightarrow$ $2 - 2 ^ { - n + 1 } = \frac { 255 } { 128 }$

$\Rightarrow$ $2 ^ { - n } = 2 ^ { - 8 }$ $\Rightarrow$ $n = 8$

Putting $n = 8$ in equation (iv),

we have or $a = 1$ .