# The Nth Term of a G.P. is 128 and the Sum of Its N Terms is 225. If Its Common Ratio is 2, Then Its First Term is - Mathematics

MCQ

The nth term of a G.P. is 128 and the sum of its n terms  is 225. If its common ratio is 2, then its first term is

#### Options

• (a) 1

• (b) 3

• (c) 8

• (d) none of these

#### Solution

$a_n = 128, S_n = 225 \text{ and } r = 2$
$a_n = 128$
$\therefore a r^\left( n - 1 \right) = 128$
$\Rightarrow 2^\left( n - 1 \right) a = 128$
$\Rightarrow \frac{2^n a}{2} = 128$
$\Rightarrow 2^n = \frac{256}{a} . . . . . . . . (i)$
$\text{ Also }, S_n = 225$
$\Rightarrow a\left( \frac{r^n - 1}{r - 1} \right) = 225$
$\Rightarrow a\left( \frac{2^n - 1}{2 - 1} \right) = 225$
$\Rightarrow a\left( \frac{256}{a} - 1 \right) = 225 \left[ \text{ Using } (i) \right]$
$\Rightarrow 256 - a = 225$
$\Rightarrow a = 256 - 225$
$\Rightarrow a = 31$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Q 12 | Page 57