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Mathematics

The general term of the G.P. 14,12,1,2,4,\dfrac{1}{4}, -\dfrac{1}{2}, 1, -2, 4, \dots is :

  1. (-1)(n - 1) × 2(n - 3)

  2. (-1)(n - 1) × 2(n - 2)

  3. (-1)(n - 1) × (-2)(n - 1)

  4. (-1)(n - 1) × (-2)(n - 3)

G.P.

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Answer

We know that,

nth term of a G.P. is given by,

Tn = arn - 1

In the given G.P.,

a = 14\dfrac{1}{4}

r = 1214\dfrac{-\dfrac{1}{2}}{\dfrac{1}{4}} = -2.

⇒ Tn = 14\dfrac{1}{4} (-2)n - 1

= 122\dfrac{1}{2^2}.(-2)n - 1

= 2-2.(-1)n - 1.(2)n - 1

= (-1)n - 1.(2) -2 + n - 1

= (-1)n - 1.(2)n - 3

Hence, option 1 is the correct option.

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