If the sum of the first $n$ terms of a series is $S_n=2n^2+5n$, then the $10$th term of the series is:

Solution

1. The $n$th term of a series is given by the formula $a_n=S_n-S_{n-1}$.
2. Calculate $$\begin{array}{rl}{S}_{10}& =2(10{)}^2+5(10)\\ & =200+50\\ & =250\end{array}$$.
3. Calculate $$\begin{array}{rl}{S}_9& =2(9{)}^2+5(9)\\ & =162+45\\ & =207\end{array}$$.
4. Subtract the values to find the 10th term: $$\begin{array}{rl}{a}_{10}& =250-207\\ & =43\end{array}$$.
5. Hence the answer is (B).