Find the first term of the G.P. whose common ratio 5 and whose su… - Vidyadip

Question

Find the first term of the G.P. whose common ratio 5 and whose sum to first 6 terms is 46872

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Answer

$\begin{aligned} & \text { Common ratio, } r=5 \\ & S _6=46872 \\ & \therefore \frac{ a \left( r ^6-1\right)}{ r -1}=46872 \\ & \Rightarrow S _6=\frac{ a \left(5^6-1\right)}{5-1}=46872 \\ & \Rightarrow a =\frac{46872 \times 4}{[25 \times 25 \times 25-1]} \\ & \Rightarrow a =\frac{187488}{15624}=12 \\ & \Rightarrow \text { first term }=12\end{aligned}$

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