A certain arithmetic sequence has this explicit formula for the nth term

Question

a_n = 13 + (n-1)(6)

The same sequence has this recursive formula

a_n = a_n-1 + ___

A. 6

B. 19

C. 13

D. 5

What is the number that goes in the blank

1. I am pretty sure its A (6) but I just want to be sure

Answer 1

You are correct. If n = 1, a₁ = 13 and if n = 2, then a₂ = 13 + 6 = 19. So each term goes up by 6. That means the recursive formula would be a_n = a_n-1 + 6