The sum to 10 terms of the series $1 \times 3^{2}+2 \times 5^{2}+3 \times 7^{2}+\ldots \ldots \ldots \ldots …
The sum to 10 terms of the series $1 \times 3^{2}+2 \times 5^{2}+3 \times 7^{2}+\ldots \ldots \ldots \ldots . .$ is
- 13,495
- $\cdot 15,595$
- $13,000$
- 13,695
Solution
$1 \times 3^{2}+2 \times 5^{2}+3 \times 7^{2}+$
Term : $\rightarrow 2(2 q+1)^{2}$
$S=\sum_{\varepsilon=1}^{10} z(2 q+1)^{2}$
$S=\sum_{\varepsilon=1}^{10}\left(4 z^{2}+4 z+1\right) \varepsilon$
$S=\sum_{z=1}^{10}\left[4 z^{3}+4 z^{2}+2\right]$
$S=\frac{4 \times 10^{2} \times 11^{2}}{4}+\frac{4 \times 10 \times 11 x}{6} +\frac{10 \times 11}{2}$
$S=13,695$
Asked in: MHT CET 2020 (20 Oct Shift 1)
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