Question

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

Answer 1

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

Answer 2

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.