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प्रश्न
Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.
उत्तर
Let the first term of the G.P. be a and its common ratio be r.
4th term =`1/18 => ar^3 = 1/18`
7th term =`1/486 => ar^6 = 1/486`
Now, `(ar^6)/(ar^3) = ((-1)/486)/(1/18)`
`=> r^3 = -1/27`
`=> r = -1/3`
`ar^3 = 1/18`
`=> a xx (-1/3)^3 = 1/18`
`=> a =- 27/18 = -3/2`
∴ G.P. = a, ar, ar2, ar3, .......
= `-3/2, -3/2 xx (-1/3), -3/2 xx (-1/3)^2, 1/18, .......`
= `-3/2, 1/2, -1/6,1/18, .......`
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