Question

The product of first three terms of a G.P. is $$-1$$ and the common ratio is $$-\frac{3}{4}$$. The sum of these three terms is ______.

Options

• $$\frac{12}{13}$$

• $$\frac{11}{13}$$

• $$\frac{11}{12}$$

• $$\frac{13}{12}$$

Answer 1

The product of first three terms of a G.P. is $$-1$$ and the common ratio is $$-\frac{3}{4}$$. The sum of these three terms is `underlinebb(13/12)`.

Explanation:

If the first term is $$a$$, then $$a^3(-3/4)^3=-1$$, giving $$a = \frac{4}{3}$$. The sum is $$a(1 + r + r^2) = \frac43\left(1-\frac34 + \frac9{16}\right) = \frac{13}{12}$$.