The given sequence is, \(\displaystyle{s}_{{n}}={2}{n}-{1}\)

a)Find the first three terms of the sequence as shown below. \(s_1 = 2(1)−1\)

\(= 2 − 1\)

\(= 1\)

\(s_2 = 2(2)−1\)

\(= 4 − 1\)

\(= 3\)

\(s_3 = 2(3)−1\)

\(= 6 − 1\)

\(= 5\) Therefore, \(s_1 = 1\)

\(s_2 = 3\)

\(s_3 = 5\)

b) The given sequence is \(\displaystyle{s}_{{n}}={2}{n}−{1}.\) The terms of the sequence are 1,3,5,7,... Here,

\(\displaystyle{s}_{{2}}-{s}_{{1}}={3}-{1}\)

\(={2}\)

\({s}_{{3}}-{s}_{{2}}={5}-{3}\)

\(={2}\)

That implies, there exists a common difference between two successive numbers. So, the given sequence is an arithmetic sequence whose common difference is \(\displaystyle{d}={2}.\)