A sequence is defined recursively by the following rules:

Question

A sequence is defined recursively by the following rules:

f(1)=3

f(n+1)=2⋅f(n)−1

Which of the following statements is true about the sequence? Select all that apply.

f(5)=33

f(3)=10

f(4)=18

f(6)=66

f(2)=5

I am confused on how I am supposed to solve this? I thought one of the anwsers was the last one but none of the others seem to line up.

Answer 1

I am not sure how to tell you to solve this problem. What I can tell you is the solution.

f(n) = 2ⁿ + 1.

However, if you just follow the recurrence relationship, you can easily get the first few terms.