Question

If the $$(p + q)$$th and $$(p - q)$$th term of a G.P. are $$m$$ and $$n$$ respectively, then its $$p$$th term is ______.

Options

• $$mn$$

• $$\sqrt{mn}$$

• $$(mn)^2$$

• $$\frac{m}{n}$$

Answer 1

If the $$(p + q)$$th and $$(p - q)$$th term of a G.P. are $$m$$ and $$n$$ respectively, then its $$p$$th term is `underlinebb(sqrt(mn))`

Explanation:

The terms equally distant from the $$p$$th term have product equal to its square: $$T_{p + q}T_{p - q} = T_p^2$$. Therefore, $$T_p=\sqrt{mn}$$ under the usual positive-term convention.