How do you find the first five terms of a sequence defined recursively

Interesting question. Good to know for computer science.

Suppose you have a function like

an = 3x - 2 Try the first couple

a1 = 3 (1) - 2

a1 = 3 - 2

a1 = 1

a2 = 3 (2) - 2

a2 = 6 - 2

a2 = 4 So each term differs by 3

a2 - a1 = 3

an = a_ (n - 1) + 3

a3 = a2 + 3

a3 = 4 + 3

a3 = 7

a4 = a3 + 3

a4 = 7 + 3

a4 = 10

a5 = a4 + 3

a5 = 10 + 3

a5 = 13

I'll do one more and then check it.

a6 = a5 + 3

a6 = 13 + 3

a6 = 16

a6 = 3x - 2

a6 = 3*6 - 2

a6 = 18 - 2

a6 = 16 which checks.

So the general formula is

an = a_ (n - 1) * k if you were multiplying or

an = a_ (n - 1) + k if you were adding. The key thing is that you are working with the previous term.