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# The first two terms of a geometric progression add up to 12. The terms of the G.P. are alternately positive and negative.The statement - The sum of the third and the fourth terms is 48 holds true for the first term being

$\begin {array} {1 1} (A)\;-4 & \quad (B)\;-12 \\ (C)\;12 & \quad (D)\;4 \end {array}$

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A)
Ans : (B)
Since $a+ar=a(1+r)=12$………………..(i)
And $ar^2+ar^3=ar^2 (1+r)=48$……………..(ii)
So, from Eqs. (i) and (ii),
$r^2=4$
$r=-2$ (terms are alternately +ve and –ve)
On putting the value of r in Eq. (i), we get
$a=-12$