Question

find a formula for the nth term in this arithmetic sequence:
(a_1 = 9), (a_2 = 13), (a_3 = 17), (a_4 = 21), ...
(a_n = ?n + quad)

Explanation:

Step1: Identify common difference $d$

$d = a_2 - a_1 = 13 - 9 = 4$

Step2: Recall arithmetic sequence formula

The general form is $a_n = a_1 + (n-1)d$

Step3: Substitute values and simplify

$$\begin{align*} a_n &= 9 + (n-1) \times 4\\ &= 9 + 4n - 4\\ &= 4n + 5 \end{align*}$$

Answer:

$a_n = 4n + 5$