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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, which of the following sequence from a G.P. :
`1/8, 1/24, 1/72, 1/216, ................`
Find the 9th term of the series :
1, 4, 16, 64, ...............
Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
For the G.P. `1/27, 1/9, 1/3, ........., 81`; find the product of fourth term from the beginning and the fourth term from the end.
Find the sum of G.P. :
0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
Q 3.2
The first term of a G.P. is –3 and the square of the second term is equal to its 4th term. Find its 7th term.
Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.
