Question

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

Explanation:

Step1: Identify first term

The first term of the sequence is $a_1 = -8$.

Step2: Calculate common difference

Find the difference between consecutive terms: $-15 - (-8) = -7$, $-22 - (-15) = -7$, so the common difference $d = -7$.

Step3: Write recursive formula

For an arithmetic sequence, the recursive formula for $n\geq2$ is $a_n = a_{n-1} + d$. Substitute $d=-7$: $a_n = a_{n-1} - 7$.

Answer:

$a_1 = -8$
$a_n = a_{n-1} - 7$ for $n \geq 2$