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प्रश्न
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
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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, ........
संबंधित प्रश्न
Find the 9th term of the series :
1, 4, 16, 64, ...............
The product of 3rd and 8th terms of a G.P. is 243. If its 4th term is 3, find its 7th term.
Find the geometric progression with 4th term = 54 and 7th term = 1458.
Q 6
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `a/x + c/y = 2`
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Find the sum of G.P. : 3, 6, 12, .........., 1536.
Find the geometric mean between `4/9` and `9/4`
Q 3.3
