Question

write a recursive formula for the following arithmetic sequence.
15, 2, -11, -24, ...
$a_1 = \square$
$a_n = \square$ for $n \geq 2$

Explanation:

Step1: Identify first term

The first term of the sequence is given as 15, so $a_1 = 15$.

Step2: Calculate common difference

Subtract consecutive terms: $2 - 15 = -13$, $-11 - 2 = -13$, $-24 - (-11) = -13$. The common difference $d = -13$.

Step3: Write recursive formula

For arithmetic sequences, the recursive formula for $n \geq 2$ is $a_n = a_{n-1} + d$. Substitute $d=-13$: $a_n = a_{n-1} - 13$.

Answer:

$a_1 = 15$
$a_n = a_{n-1} - 13$ for $n \geq 2$