Question

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

• A. ${\mathrm{n}}^2+5{\mathrm{n}}^3$
• B. ${\mathrm{n}}^3+2{\mathrm{n}}^2$
• C. $2{\mathrm{n}}^2+7{\mathrm{n}}^3$
• D. None Of These

Answer 1

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$\mathrm{n}=1$,

$$\begin{gathered} s_1={\left(1\right)}^3+2{\left(1\right)}^2=1+2=3 \\ {s}_2={\left(2\right)}^3+2{\left(2\right)}^2=8+8=16 \end{gathered}$$
$\therefore$The correct option is B.