Step 1

The given sequence is, \(s_{n} = 2n − 1\)

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,

\(s_{1} = 1\)

\(s_{2} = 3\)

\(s_{3} = 5\)

Step 2

b)The given sequence is,

\(s_{n} = 2n − 1\)

The tems of the sequence are 1,3,5,7,...

Here, \(s_{2} - s_{1} = 3 - 1\)

\(=2\)

\(s_{3} - s_{2} = 5 - 3\)

\(=2\)

That implies, there exists a common difference between two successive numbers.

So, the given sequence is an arithmetic sequence whose common difference is \(d=2\).

The given sequence is, \(s_{n} = 2n − 1\)

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,

\(s_{1} = 1\)

\(s_{2} = 3\)

\(s_{3} = 5\)

Step 2

b)The given sequence is,

\(s_{n} = 2n − 1\)

The tems of the sequence are 1,3,5,7,...

Here, \(s_{2} - s_{1} = 3 - 1\)

\(=2\)

\(s_{3} - s_{2} = 5 - 3\)

\(=2\)

That implies, there exists a common difference between two successive numbers.

So, the given sequence is an arithmetic sequence whose common difference is \(d=2\).