**Question:**

**What will be the sum of n terms of the series whose \( n^{th} \) term is \( 5.3^{n+1}+2n \)?**

Create an account

Welcome! Register for an account

A password will be e-mailed to you.

Password recovery

Recover your password

A password will be e-mailed to you.

- Advertisement -

Here \( a_n=5.3^{n+1}+2n \)

We have have to find \( s_n \).

\( \therefore s_n=\displaystyle\sum_{k=1}^{n}a_k \)

\( \therefore s_n=\displaystyle\sum_{k=1}^{n}\left(5.3^{k+1}+2k\right) \)

\( \therefore s_n=\displaystyle\sum_{k=1}^{n}5.3.3^k+\displaystyle\sum_{k=1}^{n}2k \)

\( \therefore s_n=15\displaystyle\sum_{k=1}^{n}3^k+2\displaystyle\sum_{k=1}^{n}k \)

\( \therefore s_n=15[3\left(\frac{3^n-1}{3-1}\right)]+2[\frac{n(n+1)}{2}] \)

\( \therefore s_n=\frac{45}{2}(3^n-1)+n(n+1) \)

- Advertisement -

RELATED ARTICLES

Insert math as

Additional settings

Formula color

Type math using LaTeX

Preview

\({}\)

Nothing to preview

Insert