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. $a_1 = -1$ $a_n = 4a_{n - 1}$ $a_n = $

Explanation:

Step1: Identify sequence type

This is a geometric sequence, where each term is 4 times the prior term, with first term $a_1=-1$ and common ratio $r=4$.

Step2: Recall geometric sequence formula

The explicit formula for a geometric sequence is $a_n = a_1 \cdot r^{n-1}$.

Step3: Substitute values

Substitute $a_1=-1$ and $r=4$ into the formula:
$a_n = -1 \cdot 4^{n-1}$

Step4: Simplify the expression

Rewrite to simplest form:
$a_n = -4^{n-1}$

Answer:

$a_n = -4^{n-1}$