Arithmetic series

Arithmetic series formula
Determine the sum of the first ten terms of the arithmetic series: 6 + 1 – 4 – 9 – … .
Problem involving both arithmetic sequence formula and arithmetic series formula
Find the sum of the arithmetic series: – 4 – 1 + 2 + …. + 329.
$t_{n}=s_{n}-s_{n-1}$
The sum of the first n terms of an arithmetic series is ${s_n} = 7{n^2} - 5n$ $s_{n} = 7 n^{2} - 5 n$ .
1. Find the common difference.
2. Determine the first six terms of the corresponding arithmetic sequence.
A triangle has a perimeter of 32m; the shortest side is 6 m long. If the side lengths of this triangle form an arithmetic sequence, what are the other side lengths?