Question

The sum of the first two terms of a G.P. is $$-4$$ and the fifth term is 4 times the third term. Then, the first term of the G.P. is ______.

Options

• $$-\frac{3}{4}$$ or 4

• $$\frac{3}{4}$$ or $$\frac{1}{4}$$

• $$\frac{4}{3}$$ or $$\frac{1}{4}$$

• $$-\frac{4}{3}$$ or 4

Answer 1

The sum of the first two terms of a G.P. is $$-4$$ and the fifth term is 4 times the third term. Then, the first term of the G.P. is `underlinebb(-4/3 or 4)`.

Explanation:

Let the first term be $$a$$ and ratio be $$r$$. Since $$ar^4 = 4ar^2$$, $$r = \pm2$$. Using $$a(1 + r) = -4$$ gives $$a=-\frac43$$ when $$r = 2$$ or $$a = 4$$ when $$r = -2$$.