Question

write a recursive formula for the following arithmetic sequence.
-8, -5, -2, 1, ...
$a_1 = \boxed{}$
$a_n = \boxed{}$ for $n \geq 2$

Explanation:

Step1: Identify first term

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

Step2: Find common difference

Calculate the difference between consecutive terms: $-5 - (-8) = 3$, $-2 - (-5) = 3$, $1 - (-2) = 3$. The common difference $d=3$.

Step3: Write recursive formula

For arithmetic sequences, the recursive formula for $n\geq2$ is $a_n = a_{n-1} + d$. Substitute $d=3$.

Answer:

$a_1 = -8$
$a_n = a_{n-1} + 3$ for $n \geq 2$