Question

# $3+13+29+51+79+...\mathrm{To}\mathrm{N}\mathrm{Terms}=\mathrm{_____}.$

A

${\mathrm{n}}^{2}+5{\mathrm{n}}^{3}$

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B

${\mathrm{n}}^{3}+2{\mathrm{n}}^{2}$

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C

$2{\mathrm{n}}^{2}+7{\mathrm{n}}^{3}$

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D

None Of These

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Solution

## The correct option is B ${\mathrm{n}}^{3}+2{\mathrm{n}}^{2}$Let ${\mathrm{S}}_{\mathrm{n}}=3+13+29+51+79+\dots \dots +\mathrm{n}\mathrm{terms}.$As given in the question:${\mathrm{s}}_{1}=3,{\mathrm{s}}_{2}=3+13=16,........{\mathrm{s}}_{\mathrm{n}}={\mathrm{n}}^{3}+2{\mathrm{n}}^{2}$By taking$\mathrm{n}=1$,${s}_{1}={\left(1\right)}^{3}+2{\left(1\right)}^{2}=1+2=3\phantom{\rule{0ex}{0ex}}{s}_{2}={\left(2\right)}^{3}+2{\left(2\right)}^{2}=8+8=16$$\therefore$The correct option is B.

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