The sum of first n terms of an A.P. is given by $S_n=4n^2-n$. Find ...

Question

The sum of first n terms of an A.P. is given by $S_n=4n^2-n$. Find the 25th term of this A.P.

Accepted Answer

$$a_n = S_n - S_{n-1} = (4n^2-n)-(4(n-1)^2-(n-1)) = 8n-5$$ So $a_{25}=8(25)-5=200-5=195$.