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. $a_1 = -51$ $a_n = a_{n - 1} - 7$ $a_n = $

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence with first term $a_1=-51$ and common difference $d=-7$.

Step2: Use arithmetic sequence formula

The explicit formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$.
Substitute $a_1=-51$ and $d=-7$:
$a_n = -51 + (n-1)(-7)$

Step3: Simplify the expression

Expand and combine like terms:
$a_n = -51 -7n +7$
$a_n = -7n -44$

Answer:

$a_n = -7n - 44$