Question

an arithmetic sequence is given below, -17, -12, -7, -2, ... write an explicit formula for the n^th term a_n. a_n =

Explanation:

Step1: Identify first term and common difference

The first term \( a_1 = -17 \). The common difference \( d \) is \( -12 - (-17) = 5 \).

Step2: Use arithmetic sequence formula

The explicit formula for an arithmetic sequence is \( a_n = a_1 + (n - 1)d \). Substitute \( a_1 = -17 \) and \( d = 5 \):
\( a_n = -17 + (n - 1) \times 5 \)
Simplify: \( a_n = -17 + 5n - 5 = 5n - 22 \)

Answer:

\( a_n = 5n - 22 \)