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

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 (A) 2 cos 18° (B) 2 sin 36° (C) 2 sin 18° (D) 2 cos 36°

Tardigrade Admin · Accepted Answer

a2=a3+a4 ⇒ a r=a r2+a r3 ⇒ 1=r+r2 ∴ r=(-1 ± √1+4/2)=(√5-1/2)=2 sin 18°

Q. 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

$2 cos 1 8^{\circ}$

$2 sin 3 6^{\circ}$

$2 sin 1 8^{\circ}$

$2 cos 3 6^{\circ}$

$a_{2} = a_{3} + a_{4}$
$\Rightarrow a r = a r^{2} + a r^{3}$
$\Rightarrow 1 = r + r^{2}$
$∴ r = \frac{- 1 \pm 1 + 4}{2}$
$= \frac{5 - 1}{2} = 2 sin 1 8^{\circ}$

Q. 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

2cos18∘

2sin36∘

2sin18∘

2cos36∘

a2​=a3​+a4​⇒ar=ar2+ar3 ⇒1=r+r2 ∴r=2−1±1+4​​=25​−1​=2sin18∘

$2 cos 1 8^{\circ}$

$2 sin 3 6^{\circ}$

$2 sin 1 8^{\circ}$

$2 cos 3 6^{\circ}$

$a_{2} = a_{3} + a_{4}$
$\Rightarrow a r = a r^{2} + a r^{3}$
$\Rightarrow 1 = r + r^{2}$
$∴ r = \frac{- 1 \pm 1 + 4}{2}$
$= \frac{5 - 1}{2} = 2 sin 1 8^{\circ}$