If the $(p + q)$th term of a geometric series is $m$ and the $(p - q)$th term is $n$, then the $p$th term is

Question

Dr. Abubacker · Accepted Answer

(a)
Since, $T_{p + q} = m = a(r)^{p + q - 1}$ …(i)
And $T_{p - q} = n = a(r)^{p - q - 1}$ …(ii)
On multiplying Eqs. (i) and (ii), we get
$mn = a^{2}(r)^{2p - 2}$
$\Rightarrow \ a(r)^{p - 1} = (mn)^{\frac{1}{2}}$
$	herefore\ T_{p} = (mn)^{\frac{1}{2}}$

Q. If the $(p + q)$th term of a geometric series is $m$ and the $(p - q)$th term is $n$, then the $p$th term is

Explanation

Reviewed by Dr. Abubacker

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