Question

What is the third term of the sequence defined by the recursive rule f(1)=2, f(n)=2f(n-1)+1?

Please help.

Answer 1

n = 1

f(1) = 2


f(n) = 2 f(n-1) + 1


n = 2

f(2) = 2 f(2 - 1) + 1 = 2 f(1) + 1 = 2 ∙ 2 + 1 = 4 + 1 = 5

n = 3

f(3) = 2 f(3 - 1) + 1 = 2 f(2) + 1 = 2 ∙ 5 + 1 = 10 + 1 = 11

Answer 2

11