Question

The sum of first n terms of an A.P. is 3n² + 4n. Find the 25th term of this A.P.

 

Answer 1

\[S_n = 3 n^2 + 4n\]

We know

\[a_n = S_n - S_{n - 1} \]
\[ \therefore a_n = 3 n^2 + 4n - 3 \left( n - 1 \right)^2 - 4\left( n - 1 \right)\]
\[ \Rightarrow a_n = 6n + 1\]

\[a_{25} = 6\left( 25 \right) + 1 = 151\]