Question

What is the sum of the arithmetic sequence 9, 14, 19, …, if there are 38 terms?

Answer 1

`3857`

Explanation:

The sum of an arithmetic sequence where `x_n = a +(n-1)d`
is given by `sum_(n=0)^(n=38) = n/2(2a+(n-1)d)`

In this example `a=9` and `d=5` as the first term is`9` and the difference between each term is `5`. There are `38` terms

So `sum_(n=0)^(n=38) =38/2(2*9 + 37*5) =19(18+185)=19*203`

`=3857`