Question

use the initial term and the recursive formula to find an explicit formula for the sequence $a_n$. write your answer in simplest form. $a_1 = 36$ $a_n = a_{n - 1} + 17$ $a_n = \boxed{}$

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence with first term $a_1=36$, common difference $d=17$.

Step2: Recall arithmetic sequence formula

The explicit formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$.

Step3: Substitute values into formula

Substitute $a_1=36$ and $d=17$:
$a_n = 36 + (n-1) \times 17$

Step4: Simplify the expression

Expand and combine like terms:
$a_n = 36 + 17n - 17 = 17n + 19$

Answer:

$a_n = 17n + 19$