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. $a_1 = 28$ $a_n = a_{n - 1} - 5$ $a_n = $

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence, where each term decreases by 5 (common difference $d=-5$), with first term $a_1=28$.

Step2: Recall arithmetic sequence formula

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

Step3: Substitute known values

Substitute $a_1=28$ and $d=-5$ into the formula:
$a_n = 28 + (n-1)(-5)$

Step4: Simplify the expression

$a_n = 28 -5n +5$
$a_n = 33 -5n$

Answer:

$a_n = 33 - 5n$