Question

given the following arithmetic sequence: 4, 6, 8, 10, 12, ... write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence. $a_n = \square$

Explanation:

Step1: Recall arithmetic sequence formula

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

Step2: Identify $a_1$ and $d$

For the sequence $4, 6, 8, 10, 12, \dots$, the first term $a_1 = 4$. The common difference $d$ is $6 - 4 = 2$.

Step3: Substitute into the formula

Substitute $a_1 = 4$ and $d = 2$ into the formula: $a_n = 4 + (n - 1) \times 2$.

Step4: Simplify the expression

Expand the expression: $a_n = 4 + 2n - 2 = 2n + 2$.

Answer:

$2n + 2$