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प्रश्न
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
उत्तर
Let the first term of the G.P. be a and its common ratio be r.
5th term = 81 `=>` ar4 = 81
2nd term = 24 `=>` ar = 24
Now, `(ar^4)/(ar) = 81/24`
`=> r^3 = 27/8`
`=> r = 3/2`
ar = 24
`=> a xx 3/2 = 24`
`=>` a = 16
∴ G.P. = a, ar, ar2, ar3, ..............
= `16, 24, 16 xx (3/2)^2, 16 xx (3/2)^3,.........`
= 16, 24, 36, 54, ........
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