Correct Answer - Option 1 : -13.5
Concept:
If a, b, c are in GP than \(r = \frac{b}{a} = \frac{c}{b}\)
If first term of GP is a and common ratio is r than nth term of GP is given by arn - 1
Calculation:
Given: x, 2x + 2, 3x + 3 are the first three terms of a geometric progression than
\(\frac{{2x + 2}}{x} = \frac{{3x + 3}}{{2x + 2}}\)
\(\frac{{2x + 2}}{x} = \frac{3}{2}\)
\(4x + 4 = 3x \Rightarrow x = - 4 = a\)
\(r = \frac{c}{b} = \frac{{3x + 3}}{{2x + 2}} = \frac{3}{2}\)
4th term in the geometric progression is T4= arn - 1
\({T_4} = ( - 4){\{ \frac{3}{2}\} ^{4 - 1}} = - 13.5\)
Hence, option A is the correct answer.