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The first two terms of a geometric progr...

The first two terms of a geometric progression add upto 12. The sum of the third and the fourth term is 48.If the terms of the geometric progression are alternatively positive and negative, then the first term is `:`

A

`-12`

B

12

C

4

D

`-4`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `a,ar,ar^(2),"……"`
`a+ar=12" " "…….(i)"`
and `ar^(2)+ar^(3)=48" " "…….(ii)"`
On dividing Eq. (ii) by Eq.(i), we get
`r^(2)=4," if " r ne -1`
`:. r=-2", " [:. " terms are alternatively positive and negative "]`
Now, from Eq. (i),`a=-12`.
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