In an AP, If `S_(n)=3n^(2)+5n` and `a_(k)=164,` then find the value of k.

Explanation

To solve the problem step by step, we will first find the expression for the nth term of the arithmetic progression (AP) using the given sum formula \( S_n = 3n^2 + 5n \). Then, we will find the value of \( k \) such that \( a_k = 164 \).

### Step 1: Find the nth term of the AP
The nth term \( a_n \) can be found using the formula:
\[ a_n = S_n - S_{n-1} \]
where \( S_n \) is the sum of the first \( n \) terms and \( S_{n-1} \) is the sum of the first \( n-1 \) terms.
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