The nnth term of an arithmetic sequence is \(a_{n} = a_{1}+(n-1)d\) where a_1is the first term and d is the common difference.

For the arithmetic sequence 15, 20, 25, 30, ... the first term is \(a_{1} = 15\) and the common difference is \(d = a_{2} - a_{1} = 20-15 = 5\). The nth term is then:

\(a_{n} = a_{1}+(n - 1)d\)

\(a_{n} = 15 + (n - 1)(5)\\) Substitute.

\(a_{n} = 15 +5n-5\\) Distribute.

\(a_{n} = 10 + 5n\) Combine like terms.

For the arithmetic sequence 15, 20, 25, 30, ... the first term is \(a_{1} = 15\) and the common difference is \(d = a_{2} - a_{1} = 20-15 = 5\). The nth term is then:

\(a_{n} = a_{1}+(n - 1)d\)

\(a_{n} = 15 + (n - 1)(5)\\) Substitute.

\(a_{n} = 15 +5n-5\\) Distribute.

\(a_{n} = 10 + 5n\) Combine like terms.