Question

If 2nd, 3rd and 6th terms of an A.P. are the three consecutive terms of a G.P., then the common ratio of the G.P. is ______.

Options

• 2

• 3

• $$\frac{1}{2}$$

• $$\frac{1}{3}$$

Answer 1

If 2nd, 3rd and 6th terms of an A.P. are the three consecutive terms of a G.P., then the common ratio of the G.P. is 3.

Explanation:

For the non-constant A.P. Let its first term be $$a$$ and difference be $$d$$. The three terms are $$a + d, a + 2d, a + 5d$$; the G.P. condition gives $$d = -2a$$, so their ratio is $$3$$.