Question:

Question:

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

**Answer:**

Here $a_n=5.3^{n+1}+2n$

We have have to find $s_n$.

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

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

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

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

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

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

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