# In a G.P. If the (M + N)Th Term is P and (M − N)Th Term is Q, Then Its Mth Term is - Mathematics

MCQ

In a G.P. if the (m + n)th term is p and (m − n)th term is q, then its mth term is

#### Options

• (a) 0

• (b) pq

• (c) $\sqrt{pq}$

• (d) $\frac{1}{2}(p + q)$

#### Solution

(c) $\sqrt{pq}$

$\text{ Here }, a_\left( m + n \right) = p$
$\Rightarrow a r^\left( m + n - 1 \right) = p . . . . . . . (i)$
$\text{ Also }, a_\left( m - n \right) = q$
$\Rightarrow a r^\left( m - n - 1 \right) = q . . . . . . . (ii)$
$\text{ Mutliplying } (i) \text{ and } (ii):$
$\Rightarrow a r^\left( m + n - 1 \right) a r^\left( m - n - 1 \right) = pq$
$\Rightarrow a^2 r^\left( 2m - 2 \right) = pq$
$\Rightarrow \left( a r^\left( m - 1 \right) \right)^2 = pq$
$\Rightarrow a r^\left( m - 1 \right) = \sqrt{pq}$
$\Rightarrow a_m = \sqrt{pq}$
$\text{ Thus, the } m^{th} \text{ term is } \sqrt{pq} .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Q 24 | Page 58