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

The function is defined recursively. In order to calulate f(3), f(2) and f(1) must be known. f(1) is given f(1) = 2 f(2) is then calculated f(2) = 2 * f(1) + 1 = 2 * 1 + 1 = 2 + 1 = 3 Finally f(3) can be calculated given f(2)=3 f(3)= 2 * f(2) + 1 = 2 * 3 + 1 = 6 + 1 = 7