Alg8.20

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How many terms of a GP $3,3^2,3^3,........\,$ are needed to give teh sum $120\,$

We have $S_n=\frac{3(1-3^n)}{1-3}=120\,$

$1-3^n=120\cdot\frac{-2}{3}=-80\,$

$-3^n=-81,3^n=81,3^n=3^4\,$

Hence $n=4\,$

The required number of terms is $4\,$

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