**Question:**

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

**Answer:**

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Friday, February 3, 2023

**Question:**

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

We have have to find $s_n$.

$therefore s_n=displaystylesum_{k=1}^{n}a_k$

$therefore s_n=displaystylesum_{k=1}^{n}left(5.3^{k+1}+2kright)$

$therefore s_n=displaystylesum_{k=1}^{n}5.3.3^k+displaystylesum_{k=1}^{n}2k$

$therefore s_n=15displaystylesum_{k=1}^{n}3^k+2displaystylesum_{k=1}^{n}k$

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

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

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