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.
$a_n = 57 - 3(n - 1)$, $n = 1, 2, 3...$

Explanation:

Step1: Find \(a_1\)

Substitute \(n = 1\) into \(a_n = 57 - 3(n - 1)\).
\(a_1 = 57 - 3(1 - 1) = 57 - 3(0) = 57\).

Step2: Find \(a_2\)

Substitute \(n = 2\) into the formula.
\(a_2 = 57 - 3(2 - 1) = 57 - 3(1) = 54\).

Step3: Find \(a_3\)

Substitute \(n = 3\) into the formula.
\(a_3 = 57 - 3(3 - 1) = 57 - 3(2) = 51\).

Step4: Find \(a_4\)

Substitute \(n = 4\) into the formula.
\(a_4 = 57 - 3(4 - 1) = 57 - 3(3) = 48\).

Answer:

\(57, 54, 51, 48\)