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Mathematics

Find the sum of G.P. :

1 + 3 + 9 + 27 + …….. to 12 terms

GP

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Answer

Common ratio (r) = 31\dfrac{3}{1} = 3.

S=a(rn1)(r1)..........(Asr>1)=1(3121)31=53144112=5314402=265720.S = \dfrac{a(r^n - 1)}{(r - 1)} ……….(As |r| \gt 1)\\[1em] = \dfrac{1(3^{12} - 1)}{3 - 1} \\[1em] = \dfrac{531441 - 1}{2} \\[1em] = \dfrac{531440}{2} \\[1em] = 265720.

Hence, sum = 265720.

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