Question

The sum of first n terms of an A.P is 5n² + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.

Answer 1

$$\begin{gathered} S_n=5n^2+3n \\ \mathrm{We}\mathrm{know} \\ {a}_n=S_n-S_{n-1} \\ \therefore a_n=5n^2+3n-5{\left(n-1\right)}^2-3\left(n-1\right) \\ {a}_n=10n-2 \end{gathered}$$

Now,

$$\begin{gathered} a_m=168 \\ \Rightarrow 10m-2=168 \\ \Rightarrow 10m=170 \\ \Rightarrow m=17 \end{gathered}$$

$a_{20}=10\left(20\right)-2=198$