Question

Write a rule for the arithmetic sequence below (hint: the y values are listed and the x values are implied as 1,2,3,4...)

3, 1, -1, -3

Answer 1

a(n) = 3 - 2(n - 1)

Explanation:

In the sequence 3, 1, -1, -3, each new term is found by subtracting 2 from the previous term. For example: -1 came from subtracting 2 from +1.

The first term is 3 and the common difference is 2.

The general arithmetic sequence formula is a(n) = a(1) + 2(n - 1).

In this case:

The first term is 3 and the common difference is 2. Thus, the formula for this arithmetic sequence is

a(n) = 3 - 2(n - 1)