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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 G.P. whose first term is 64 and next term is 32.
If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.
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.
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
Q 6
Find the sum of G.P. :
1 + 3 + 9 + 27 + .......... to 12 terms.
Find the sum of G.P. :
0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Q 8
