If the $(p + q)^{t h}$ term of a geometric series is m and the $(p - q)^{t h}$ term is n then the $p^{t h}$ term is

(m n)^{1 / 2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

m+n

No worries! We‘ve got your back. Try BYJU‘S free classes today!

m-n

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $(m n)^{1 / 2}$
Given,

$(p + q) t h$ term is $m$

$(p - q) t h$ term is $n$

we have,

$A R^{p + q - 1} = m$ ,

$\Rightarrow A R^{p - 1} R^{q} = m$ ......(1)

$A R^{p - q - 1} = n$

$\Rightarrow A \frac{R^{p - 1}}{R^{q}} = n$ .....(2)

multiplying (1) and (2)

$m n = A R^{p - 1} R^{q} \times A \frac{R^{p - 1}}{R^{q}}$

$m n = (A R^{p - 1})^{2}$

$∴ A R^{p - 1} = \sqrt{m n}$

Suggest Corrections

Similar questions

If the $(p + q)^{t h}$ term of a G.P. is m and $(p - q)^{t h}$ term is n, then pth term will be _____.

(p + q)^{t h}

(p - q)^{t h}

p^{t h}

If the $(p + q)^{t h}$ term of a G.P. is m and $(p - q)^{t h}$ term is n, then pth term will be _____.

If $(p + q)^{th}$ term and $(p - q)^{th}$ term of a G.P. be $m$ and $n,$ then the $p^{th}$ term will be ___.

If $(p + q)^{t h}$ and (p - q)th terms of a G.P. are m and n respectively, then write its pth term.

Join BYJU'S Learning Program