Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the G.P. Consider that each term of the G.P. is positive.
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Let the first term be a and common ratio be r.
2nd term = ar = 6
5th term = 9*3rd term
= > ar^4 = 9 * ar^2
= > r^2 = 9
= > r = 3 { r can't be -ve here }
Hence, 2nd term = 6
= > ar = 6
= > a(3) = 6
= > a = 2
Therefore, GP is
= > a = 2
= > ar = 6
= > ar^2 = (2)(3^2) = 18
GP is 2, 6, 18, ...
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