Question

Generate the first 5 terms of this sequence:. f(1) = 0 and f(2) = 1, f(n) = f(n - 1) + f(n - 2), for n > 2. A. 0, -1, 1, 0, 2. B. 0, 1, 1, 2, 3. C. 0, 1, 2, 2, 3. D. 0, 1, 1, 2, 2.

Answer 1

You are given a function of f(n) = f(n - 1) + f(n - 2) where f(1) = 0 and f(2) = 1. You are asked to generate the first five terms of this sequence. All you need to do is to substitute the value of n greater than 2.

for n = 3
f(3) = f(3 - 1) + f(3 - 2)
f(3) = f(2) + f(1)
since f(2) = 1 and f(1) = 0
so, f(3) = 1 + 0 = 1

for n = 4
f(4) = f(4 - 1) + f(4 - 2)
f(4) = f(3) + f(2)
you have solved that for f(3) = 1 and since f(2) = 1
so, f(4) = 1 + 1 = 2

for n = 5
f(5) = f(5 - 1) + f(5 - 2)
f(5) = f(4) + f(3)
you have solved that for f(4) = 2 and f(3) = 1
so, f(5) = 2 + 1 = 3

the sequence is 0, 1, 1, 2, 3 so the answer is letter B

Answer 2

Given the f(2) = 1 and f(1) = 0. The value of f(3) may be calculated by,
f(3) = f(2) + f(1) = 1 + 0 = 1
For f(4),
f(4) = f(3) + f(2) = 1 + 1 = 2
For f(5),
f(5) = f(4) + f(3) = 2 + 1 = 3

Thus, the terms are 0, 1, 1, 2, and 3. The answer is letter B.