Question

How do you find `S_n` for the arithmetic series given `a_n=23/10`, d=1/5, n=10?

Answer 1

`s_10 = 14`

Explanation:

Our first order of business is to find the starting term, `a` of the series, because it will be needed to find the sum, not matter which formula we use.

`t_n = a + (n - 1)d`

`23/10 = a + (10 - 1)(1/5)`

`23/10 = a + 9/5`

`23/10 - 9/5 = a`

`5/10 = a`

`a = 1/2`

The sum is given by the formula `s_n = n/2(a + t_n)`.

`s_10 = 10/2(1/2 + 23/10)`

`s_10 = 5(28/10)`

`s_10 = 28/2`

`s_10 = 14`

Hopefully this helps!