Question

How do you find the sum of the arithmetic sequence. -1, 2, 5, 8, 11, 14, 17?

Answer 1

Just add them or use process as given below. Sum is `56`.

Explanation:

An arithmetic sequence is of type `a, a+d, a+2d, a+3d, ....`
in which first term is `a` and difference between a term and its preceding term is `d`.

`n^(th)` term of such a sequence is `a+(n-1)d` and sum of the series up to `n` terms is given by `an+n(n-1)d/2`

In arithmetic sequence. `{-1, 2, 5, 8, 11, 14, 17, .........}`, `a=-1` and `d=3`, hence of first `n` terms is `-n+(3n(n-1))/2`, whic can be simplified to `(-2n+3n^2-3n)/2` or

`(3n^2-5n)/2`.

As there are `7` terms in the series, their sum is `(3*7^2-5*7)/3` or `(147-35)/2` or `112/2` or `56`.