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

This is a recursive function so it uses the answer from the previous value to get the new value.

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

f (1) = 2

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

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

f (2) = 2 f (1) + 1

f (2) = 2 (2) + 1

f (2) = 5

f (3) = 2 (5) + 1

f (3) = 11

2, 5, 11,

11 is the third term.

F (3) = 4 since f (1) = 2 you need to get to f (3) by adding 1 each time you increase n.