An algebra problem by kritarth lohomi

$n$ th term of the given series is $t_{n} = S_{n}-S_{n-1}=n^2+n-1-(n-1)^2-(n-1)+1=2n$ .

So, $t_{2}=2*2=\boxed{4}$

Second term= $S_{2}$ - $S_{1}$ =( $2^2$ + 2 - 1) - ( $1^2$ + 1 - 1)=5 - 1 = 4

for n=1, sum of the first term (or the first term itself)= 1^2 +1-1 =1

for n=2, sum of first 2 terms= 2^2 +2-1 =5

now, the first term is 1, so the second term is 5-1 =4