IP1U7 HOT Q8

An arithmetic sequence is such that each term in the sequence is found by adding the same number (known as the common difference) to the previous term. The sum of the terms of an arithmetic sequence is called arithmetic series.

For an arithmetic sequence with first term \(a\), common difference \(d\), find

1. an expression, in terms of \(n\), for the \({{n}^{\mathrm{th}}}\) term, \({{T}_{n}}\), of this arithmetic sequence;
2. an expression, in terms of \(a\), \(d\) and \(n\), for the arithmetic series, \({{S}_{n}}\), as the sum of first \(n\) terms of the sequence.