Question

4) A sequence is defined recursively by f(1) = 2

and f(n) = 3f(n-1) + 1. Find the first three
terms of the sequence.

- How do I do this question and just Recursive Sequences in general?

Answer 1

The first 3 terms are 2, 7, 22.

Explanation:

The n is the sequence number of the term: f(1) means the first term.

The second term

f(2) = 3f(n - 1) + 1 We make n = 2:

= 3f(2-1) + 1

= 3f(1) + 1 f(1) = 2 so:

= 3*2 + 1

= 7.

3rd term f(3)

= 3f(3 - 1) + 1

= 3f(2) + 1

= 3(7) + 1

= 22.

Answer 2

`S=[2,7,22,\dots]`.

Let me explain why.

`f(1)=2` this is our first term.

`f(2)=3f(2-1)+1=3f(1)+1=7` second term.

`f(3)=3f(3-1)+1=3f(2)+1=22` third term.

...

Pretty simple huh?

Hope this helps.