Question

write a recursive formula for the following arithmetic sequence. -29, -22, -15, -8, ...
$a_1 = \square$
$a_n = \square$ for $n \geq 2$

Explanation:

Step1: Identify first term

The first term $a_1$ is the first value in the sequence.
$a_1 = -29$

Step2: Calculate common difference

Find the difference between consecutive terms.
$d = -22 - (-29) = 7$

Step3: Write recursive formula

For arithmetic sequences, $a_n = a_{n-1} + d$ for $n\geq2$.
$a_n = a_{n-1} + 7$

Answer:

$a_1 = -29$
$a_n = a_{n-1} + 7$ for $n \geq 2$