Question

In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is ______.

Options

• sin 18°

• 2 cos18°

• cos 18°

• 2 sin 18°

Answer 1

In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is 2 sin 18°.

Explanation:

Since t_n = t_n+1 + t_n+2

⇒ ar^n–1 = arⁿ + arⁿ⁺¹

⇒ 1 = r + r²

r = `(-1 +- sqrt(5))/2`

Since r > 0

Therefore, r = `2 (sqrt(5) - 1)/4`

= 2 sin 18°