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प्रश्न
Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.
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उत्तर
Let the five terms of the given G.P. be
`a/(r^2), a/r, a, ar, ar^2`
Given, sum of first two terms = – 4
`a/(r^2) + a/r = 4`
`=> (a + ar)/r^2 = -4`
`=> a + ar = -4r^2`
`=> a(1 + r) = -4r^2`
`=> a = -(4r^2)/(1 + r)`
And 5th term = 4(3rd term)
`=>` ar2 = 4(a)
`=>` r2 = 4
`=>` r = ±2
When r = +2,
`a = -(4(2)^2)/(1 + 2) = -16/3`
When r = –2,
`a = -(4(-2)^2)/(1 - 2) = -16`
Thus, the required terms are `a/(r^2), a/r, a, ar, ar^2`
i.e `(-16/3)/4, (-16/3)/2, -16/3, -16/3 xx 2, -16/3 xx 4` OR `16/4, 16/(-2), 16, 16(-2), 16 xx 4`
i.e `-4/3, -8/3, -16/3, -32/3, -64/3` OR `4, -8, 16, -32, 64`
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