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The product of three consecutive terms o...

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the secon of these terms, the three terms now form an A.P. . Then the sum of the original three terms of the given G.P. is

A

36

B

28

C

32

D

24

Text Solution

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The correct Answer is:
B
Let the three consecutive terms of a GP are `(a)/(r)`, a and ar.
Now, according to the question, we have
`(a)/(r).a.ar = 512`
`rArr a^(3) = 512`
`rArr a = 8`...(i)

Also, after adding 4 to first two terms, we get
`(8)/(r) + 4, 8 + 4, 8r` are in AP
`rArr 2(12) = (8)/(r) + 4 + 8r`
`rArr 24 = (8)/(r) + 8r + 4 " " 20 = 4 ((2)/(r) + 2r)`
`rArr 5 = (2)/(r) + 2r " " 2r^(2) - 5r + 2 = 0`
`rArr 2r^(2) - 4r - r + 2 = 0`
`rArr 2r (r -2) - 1 (r -2) = 0`
`rArr (r - 2) (2r -1) = 0`
`rArr (r -2) (2 -1) = 0`
`rArr r = 2, (1)/(2)`
Thus, the terms are either 16, 8 4 or 4, 8, 16. Hence, required sum = 28
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