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Question
Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
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Solution
Let the first term of the G.P. be a and its common ratio be r.
Now, 2nd term = t2 = 6 `=>` ar = 6
Also, t5 = 9 × t3
`=>` ar4 = 9 × ar2
`=>` r2 = 9
`=>` r = ±3
Since, each term of a G.P. is positive, we have r = 3 and ar = 6
`=>` a × 3 = 6
`=>` a = 2
∴ G.P. = a, ar, ar2, ar3, ........
= 2, 6, 2 × (3)2, 2 × (3)3, ............
= 2, 6, 18, 54, ..........
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