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Mathematics

(2x + 2) and (3x + 3) are two consecutive terms of a G.P. The common ratio of the G.P. is :

  1. 2

  2. 3

  3. 32\dfrac{3}{2}

  4. 23\dfrac{2}{3}

AP GP

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Answer

By formula,

Common ratio = an+1an\dfrac{a{n + 1}}{an}

Given,

(2x + 2) and (3x + 3) are two consecutive terms of a G.P.

∴Common ratio =3x+32x+2=3(x+1)2(x+1)=32.\therefore \text{Common ratio } = \dfrac{3x + 3}{2x + 2} \\[1em] = \dfrac{3(x + 1)}{2(x + 1)} \\[1em] = \dfrac{3}{2}.

Hence, Option 3 is the correct option.

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