In an AP, if sn = 3n2 + 5n and

$\because n$th term of an AP,

$a_{n}=S_{n}-S_{n-1}$

$=3 n^{2}+5 n-3(n-1)^{2}-5(n-1)$   $\left[\because S_{n}=3 n^{2}+5 n\right.$ (given) $]$

$=3 n^{2}+5 n-3 n^{2}-3+6 n-5 n+5$

$a_{n}=6 n+2$ $\ldots($ i)

or $a_{k}=6 k+2=164$ $\left[\because a_{k}=164\right.$ (given))

$\Rightarrow \quad 6 k=164-2=162$

$\therefore \quad k=27$