1. Tardigrade
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  4. The first two terms of a geometric progression add up to 12 the sum of the third and the fourth terms is 48 . If the terms of the geometric progression are alternately positive and negative, then the first term is

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Q. The first two terms of a geometric progression add up to $12$ the sum of the third and the fourth terms is $48$ . If the terms of the geometric progression are alternately positive and negative, then the first term is

Sequences and Series

Solution:

As per question, $a+a r=12\, \dots(i)$
$a r^{2}+a r^{3}=48 \, \dots(ii)$
$\Rightarrow \frac{a r^{2}(1+r)}{a(1+r)}=\frac{48}{12}$
$ \Rightarrow r^{2}=4$,
$\Rightarrow r=-2$
$ \Rightarrow a=-12$
$( \because$ terms are + ve and - ve alternately )