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Mathematics

The sum of 7 terms of the G.P. 3, 6, 12, ………. is :

  1. 181

  2. 241

  3. 381

  4. 421

G.P.

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Answer

In the given G.P.,

a = 3

r = 63\dfrac{6}{3} = 2

n = 7

Formula for sum of n terms of a G.P.

Sn=a(rn1)r1S_n = \dfrac{a(r^n-1)}{r-1} [r > 1]

Substituting values we get :

S7=3(271)21=3(271)1=3(1281)=3×(127)=381.\Rightarrow S_7 = \dfrac{3(2^7 - 1)}{2-1} \\[1em] = \dfrac{3(2^7 - 1)}{1} \\[1em] = 3(128 - 1) \\[1em] = 3 \times (127) \\[1em] = 381.

Hence, option 3 is the correct option.

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