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. $a_1 = 300$ $a_n = 3a_{n - 1}$ $a_n = \square$

Explanation:

Step1: Identify sequence type

This is a geometric sequence with first term $a_1=300$ and common ratio $r=3$.

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 $a_1=300$ and $r=3$ into the formula:
$a_n = 300 \cdot 3^{n-1}$

Step4: Simplify the expression

Rewrite $300 \cdot 3^{n-1}$ as $100 \cdot 3 \cdot 3^{n-1} = 100 \cdot 3^n$

Answer:

$a_n = 100 \cdot 3^n$