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 ______. - Mathematics

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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 ______.

• sin 18°

• 2 cos18°

• cos 18°

• 2 sin 18°

Solution

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 tn = tn+1 + tn+2

⇒ arn–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°

Concept: Geometric Progression (G. P.)
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APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 9 Sequences and Series
Solved Examples | Q 16 | Page 158