If the (p + q)th and (p – q)th terms of a GP are m and n respectively,

Question:

If the (p + q)th and (p – q)th terms of a GP are m and n respectively, find its pth term. 

Solution:

Let,

$t_{p+q}=m=A r^{p+q-1}=A r^{p-1} r^{q}$

And

$t_{p-q}=n=A r^{p-q-1}=A r^{p-1} r^{-q}$

We know that $\mathrm{p}^{\text {th }}$ term $=\mathrm{Ar}^{\mathrm{p}-1}$

$\therefore m \times n=A^{2} r^{2 p-2}$

$\Rightarrow \mathrm{Ar}^{\mathrm{p}-1}=(\mathrm{mn})^{1 / 2}$

$\Rightarrow \mathrm{p}^{\text {th }}$ term $=(\mathrm{mn})^{1 / 2}$

Ans: $p^{\text {th }}$ term $=(m n)^{1 / 2}$

 

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