Question

functions and lines
finding the first terms of an arithmetic sequence using an explicit rule
find the first four terms of the sequence given by the following.
$a_n = 31 + 4(n - 1)$, $n = 1, 2, 3...$

Explanation:

Step1: Find \(a_1\) (n=1)

Substitute \(n = 1\) into \(a_n = 31 + 4(n - 1)\):
\(a_1 = 31 + 4(1 - 1) = 31 + 4(0) = 31\)

Step2: Find \(a_2\) (n=2)

Substitute \(n = 2\) into the formula:
\(a_2 = 31 + 4(2 - 1) = 31 + 4(1) = 35\)

Step3: Find \(a_3\) (n=3)

Substitute \(n = 3\):
\(a_3 = 31 + 4(3 - 1) = 31 + 4(2) = 31 + 8 = 39\)

Step4: Find \(a_4\) (n=4)

Substitute \(n = 4\):
\(a_4 = 31 + 4(4 - 1) = 31 + 4(3) = 31 + 12 = 43\)

Answer:

31, 35, 39, 43