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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°
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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°
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