College Algebra, Chapter 9, 9.2, Section 9.2, Problem 24

Determine the first five terms of the sequence $\displaystyle a_n = 1 + \frac{n}{2}$ and tell whether it is arithmetic. If it is arithmetic, find the common difference, and express the nth term of the sequence in the standard form $a_n = a + (n - 1)d$.

The first five terms of the sequence


$
\begin{equation}
\begin{aligned}

a_1 =& 1 + \frac{1}{2} = \frac{3}{2}
\\
\\
a_2 =& 1 + \frac{2}{2} = 2
\\
\\
a_3 =& 1 + \frac{3}{2} = \frac{5}{2}
\\
\\
a_4 =& 1 + \frac{4}{2} = 3
\\
\\
a_5 =& 1 + \frac{5}{2} = \frac{7}{2}

\end{aligned}
\end{equation}
$


Here the difference is $\displaystyle d = \frac{1}{2}$ and $\displaystyle a = \frac{3}{2}$. So the nth term is $\displaystyle a_n = \frac{3}{2} + (n - 1) \frac{1}{2}$.