Question

What is the arithmetic sequence if the y value is going up by 1 and the x goes up by 7 on points (0, 13), (1, 20), and (2, 27)?

Answer 1

The y-values form the arithmetic sequence 13, 20, 27, ... with common difference 7.

As a function of x (with x = 0,1,2,...): y = 13 + 7x.
If you prefer sequence index n starting at 1 (a1 = 13): a_n = 13 + 7(n − 1) = 7n + 6.

(Also: y increases by 7 when x increases by 1, so the slope is 7.)