Question

question what is a formula for the nth term of the given sequence? 4, 1, -2... answer $a_n = 7 - 3n$ $a_n = 1 - 3(n - 1)$ $a_n = 1 + 3n$ $a_n = 4(-3)^{n - 1}$ submit answer

Explanation:

Step1: Identify the sequence type

This is an arithmetic - sequence as the difference between consecutive terms is constant. The first term $a_1 = 4$, and the common difference $d=1 - 4=-3$.

Step2: Recall the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is $a_n=a_1+(n - 1)d$.

Step3: Substitute values into the formula

Substitute $a_1 = 4$ and $d=-3$ into the formula:
$a_n=4+(n - 1)(-3)=4-3n + 3=7-3n$.

Answer:

$a_n = 7 - 3n$