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Mathematics

The common ratio of a G.P., whose 4th term is 27 and 6th term is 243; is :

  1. 9

  2. 3

  3. 13\dfrac{1}{3}

  4. 19\dfrac{1}{9}

AP GP

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Answer

Let first term of G.P. be a and common ratio be r.

By formula,

⇒ an = arn - 1

Given,

4th term of G.P. is 27.

⇒ a4 = 27

⇒ ar4 - 1 = 27

⇒ ar3 = 27 ……..(1)

Given,

6th term of G.P. is 243.

⇒ a6 = 243

⇒ ar6 - 1 = 243

⇒ ar5 = 243 ……..(2)

Dividing equation (2) by (1), we get :

ar5ar3=24327r2=9r=9=3.\Rightarrow \dfrac{ar^5}{ar^3} = \dfrac{243}{27} \\[1em] \Rightarrow r^2 = 9 \\[1em] \Rightarrow r = \sqrt{9} = 3.

Hence, Option 2 is the correct option.

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