The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its

Answer: Option B

$$\begin{array}{rl}& \text{Sum}\text{of}n\text{terms}\left(S_n\right)=3n^2+5n\\ & \therefore \text{Sum}\text{of}\left(n-1\right)\text{terms}\left(S_{n-1}\right)\\ & =3{\left(n-1\right)}^2+5\left(n-1\right)\\ & =3\left(n^2-2n+1\right)+5n-5\\ & =3n^2-6n+3+5n-5\\ & =3n^2-n-2\\ & \therefore n^{th}\text{term}=S_n-S_{n-1}\\ & \Rightarrow a_n=3n^2+5n-3n^2+n+2\\ & a_n=6n+2,\text{But}{a}_n=164\\ & \Rightarrow 6n+2=164\\ & \Rightarrow 6n=164-2\\ & \Rightarrow 6n=162\\ & \therefore n=\frac{162}{6}=27^{th}\text{term}\end{array}$$