First slide

Geometric progression

Question

$If (p + q)^{th} term of a G.P. is ' a' and its (p - q)^{th} term is 'b' where a, b \in R^{+},$ $then its p^{th} term is$

Moderate

A

$\sqrt{\frac{a^{3}}{b}}$
B

$\sqrt{\frac{b^{3}}{a}}$
C

$\sqrt{a b}$
D

$- \sqrt{a b}$

Solution

Let ‘A’ be first term and ‘r’ be the common ratio. We have.
$\begin{array}{l} a = A r^{p + q - 1}, b = A r^{p - q - 1} \\ \Rightarrow a b = A^{2} \times r^{2 p - 2} \\ \Rightarrow \sqrt{a b} = A r^{p - 1} = p^{t h} term \end{array}$

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