Question

The third term of a G.P. is the square of its first term. If its third term is 8, then the common ratio is ____________.

Answer 1

Let the G.P be a, ar, ar²
According to given condition,
third term = (first term)²
i.e ar² = a²
i.e r² = a (1)
given ar² = 8 (given)
i.e a² = 8
$\mathrm{i}.\mathrm{e}a=\sqrt{8}$