If x, 2x + 2, 3x + 3 are the first three terms of a geometric progression, then 4<sup>th</sup> term in the geometric progression is
For a GP: \((2x + 2)^2 = x(3x + 3) \Rightarrow 4(x+1)^2 = 3x(x+1)\).
\(x = -1\) makes the terms 0, which is not allowed. So \(4(x + 1) = 3x \Rightarrow x = -4\).
The terms are −4, −6, −9, with ratio \(\frac{3}{2}\).
4th term = \(-9 \times \frac{3}{2} = -13.5\)
Answer: (A) −13.5
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