If x, 2x + 2, 3x + 3 are the first three terms of a geometric progress

1.	If x, 2x + 2, 3x + 3 are the first three terms of a geometric progression, then 4th term in the geometric progression is1. -13.52. 13.53. -274. 27
Answer» 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 ar^{n - 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= ar^{n - 1} \({T_4} = ( - 4){\{ \frac{3}{2}\} ^{4 - 1}} = - 13.5\) Hence, option A is the correct answer.

If x, 2x + 2, 3x + 3 are the first three terms of a geometric progression, then 4th term in the geometric progression is1. -13.52. 13.53. -274. 27

Answer» 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 ar^{n - 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= ar^{n - 1}

\({T_4} = ( - 4){\{ \frac{3}{2}\} ^{4 - 1}} = - 13.5\)

Hence, option A is the correct answer.

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