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प्रश्न
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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उत्तर
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, ..........
संबंधित प्रश्न
Find the G.P. whose first term is 64 and next term is 32.
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
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.
The fourth term, the seventh term and the last term of a geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and number of terms.
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Find the sum of G.P. :
`(x + y)/(x - y) + 1 + (x - y)/(x + y) + ..........` upto n terms.
Find the sum of G.P. : 3, 6, 12, .........., 1536.
