Question

write a recursive formula for the following arithmetic sequence. 24, 19, 14, 9, ...
$a_1 = \square$
$a_n = \square$ for $n \geq 2$

Explanation:

Step1: Identify first term

The first term $a_1$ is the first value in the sequence.
$a_1 = 24$

Step2: Find common difference

Calculate the difference between consecutive terms.
$19 - 24 = -5$, $14 - 19 = -5$, $9 - 14 = -5$

Step3: Write recursive formula

For arithmetic sequences, $a_n = a_{n-1} + d$ where $d$ is the common difference.
$a_n = a_{n-1} - 5$ for $n \geq 2$

Answer:

$a_1 = 24$
$a_n = a_{n-1} - 5$ for $n \geq 2$