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Q.
If $x, 2 x+2,3 x+3$ are in G.P., then the fourth term is
Sequences and Series
Solution:
$x, 2 x+2,3 x+3$ are in $G.P$.
$\Rightarrow (2 x+2)^{2}=x(3 x+3)$
$\Rightarrow 4 x^{2}+8 x+4=3 x^{2}+3 x$
$\Rightarrow x^{2}+5 x+4=0$
$\Rightarrow x=-1,-4$
So, the GP is $-4,-6,-9, \ldots$
(considering $x=-4,$ as for $x=-1$ $2 x+2=0)$
Hence, fourth term is $-9 \times 1.5=-13.5$