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Question
Find the geometric progression with 4th term = 54 and 7th term = 1458.
Solution
Let the first term of the G.P. be a and its common ratio be r.
4th term = 54 `=>` ar3 = 54
7th term = 1458 `=>` ar6 = 1458
Now, `(ar^6)/(ar^3) = 1458/54`
`=>` r3 = 27
`=>` r = 3
ar3 = 54
`=>` a × (3)3 = 54
`=> a = 54/27 = 2`
∴ G.P. = a, ar, ar2, ar3, ........
= 2, 2 × 3, 2 × (3)2, 54, ...........
= 2, 6, 18, 54, ............
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