[Math] Finding the sum of arithmetic series when last term and common difference is given .

Question

The last term of an arithmetic series of 20 terms is 195 and common difference is 5. Calculate the sum of the series.

Answer 1

The $n$th term of an arithmetic series is given by $$T_n=a+(n-1)d$$where $T_n$ is the $n$th term. If you know $n$, the last term and $d$ you can use this to calculate a value for $a$, the first number. From here you can you the summation formula for an arithmetic series that is $$S_n=\frac{n}{2}\big(2a+(n-1)d\big)$$ where $S_n$ is the sum of the series.