Generate the first 5 terms of this sequence:
f(1) = 2 and f(2) = 3, f(n) = f(n - 1) + f(n - 2), for n > 2. (1 point)
a) 2, 3, 5, 7, 9
b) 2, 3, 4, 7, 11
c) 2, 3, 5, 9, 11
d) 2, 3, 5, 8, 13
your formula is interpreted this way
f(3) = f(2) + f(1)
f(4) = f(3) + f(2)
f(5) = f(4) + f(3)
etc
so f(3) = 3 + 2 = 5
f(4) = .......
notice we already eliminated b)
continue ....
btw, this is a famous sequence called the Fibonacci sequence, one of my favourite topics in Math.
To generate the first 5 terms of the given sequence, we'll use the recursive formula f(n) = f(n - 1) + f(n - 2), where f(1) = 2 and f(2) = 3.
Step 1: Starting with the first two terms given, f(1) = 2 and f(2) = 3.
Step 2: Apply the recursive formula to find the third term, f(3):
f(3) = f(3-1) + f(3-2) = f(2) + f(1) = 3 + 2 = 5.
Step 3: Apply the recursive formula again to find the fourth term, f(4):
f(4) = f(4-1) + f(4-2) = f(3) + f(2) = 5 + 3 = 8.
Step 4: Apply the recursive formula once more to find the fifth term, f(5):
f(5) = f(5-1) + f(5-2) = f(4) + f(3) = 8 + 5 = 13.
Therefore, the first 5 terms of the sequence are 2, 3, 5, 8, 13.
Among the answer choices provided:
a) 2, 3, 5, 7, 9
b) 2, 3, 4, 7, 11
c) 2, 3, 5, 9, 11
d) 2, 3, 5, 8, 13
We can see that the correct answer is option d) 2, 3, 5, 8, 13.