Question

what is the \\(n^{\text{th}}\\) term rule for this arithmetic sequence?

5, 7, 9, 11, ...

Explanation:

Identify the terms of the sequence

$$ a_1 = 5, \quad a_2 = 7, \quad a_3 = 9, \quad a_4 = 11 $$

Calculate the common difference

$$ d = a_2 - a_1 = 7 - 5 = 2 $$

Find the nth term formula

$$ a_n = a_1 + (n - 1)d = 5 + (n - 1)2 = 2n + 3 $$

Answer:

\(2n + 3\)