Question

How do you find `S_n` for the arithmetic series given `a_1=4`, a_n=100# and n=25?

Answer 1

`S_n=650`

Explanation:

An arithmetic series with first term as `a_1`, common diffeence as `d` has `n^(th)` term `a_n=a_1+(n-1)d` and its sum `S_n` is given by

`S_n=n/2(a_1+a_n)=n/2(2a+(n-1)d)`

Here, we have `a_1=4`, `a_n=100` and `n=25`, hence

`S_n=25/2(4+100)=25/2xx104=650`