Question

The product of first five terms of a G.P. with first term a and common ratio r > 1 is equal to ______.

Options

• $$\frac{a(r^{5} - 1)}{(r - 1)}$$

• $$ar^{4}$$

• $$a^{5}r^{10}$$

• $$\frac{a(r^{5} - 1)}{r}$$

Answer 1

The product of first five terms of a G.P. with first term a and common ratio r > 1 is equal to a⁵r¹⁰.

Explanation:

The five terms are $$a, ar, ar^2, ar^3, ar^4$$. Their product is $$a^5r^{0 + 1 + 2 + 3 + 4} = a^5r^{10}$$.