Question

write a recursive formula for the following arithmetic sequence.
-2, -8, -14, -20, ...
$a_1 = \boxed{}$
$a_n = \boxed{}$ for $n \geq 2$

Explanation:

Step1: Identify first term

The first term $a_1$ of the sequence is the first given value.
$a_1 = -2$

Step2: Calculate common difference

Find the difference between consecutive terms.
$d = -8 - (-2) = -6$

Step3: Write recursive formula

For arithmetic sequences, $a_n = a_{n-1} + d$ for $n\geq2$. Substitute $d=-6$.
$a_n = a_{n-1} - 6$

Answer:

$a_1 = -2$
$a_n = a_{n-1} - 6$ for $n \geq 2$