Question

write a recursive formula for the following arithmetic sequence. -7, -3, 1, 5, ...
$a_1 = \square$
$a_n = \square$ for $n \geq 2$

Explanation:

Step1: Identify first term

$a_1 = -7$

Step2: Calculate common difference

$d = -3 - (-7) = 4$

Step3: Write recursive formula

For arithmetic sequences, $a_n = a_{n-1} + d$ for $n\geq2$. Substitute $d=4$:
$a_n = a_{n-1} + 4$

Answer:

$a_1 = -7$
$a_n = a_{n-1} + 4$ for $n \geq 2$