Question

what is a formula for the nth term in the sequence 12, 20, 28, ...?
$a_{n} = 12 + 8(n - 1)$
$a_{n} = 4 + 8(n - 1)$
$a_{n} = 20 + 8(n - 1)$
$a_{n} = 12(8)^{n}$

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence, where each term increases by a constant difference. The general formula for the nth term of an arithmetic sequence is $a_n = a_1 + d(n-1)$, where $a_1$ is the first term, and $d$ is the common difference.

Step2: Find $a_1$ and $d$

The first term $a_1 = 12$. Calculate the common difference: $d = 20 - 12 = 8$.

Step3: Substitute into formula

Substitute $a_1=12$ and $d=8$ into the arithmetic sequence formula: $a_n = 12 + 8(n-1)$.

Step4: Verify with given terms

For $n=2$: $a_2 = 12 + 8(2-1) = 20$, which matches. For $n=3$: $a_3 = 12 + 8(3-1) = 28$, which matches.

Answer:

A. $a_n = 12 + 8(n - 1)$