Question
A sequence is defined recursively using the formula . If the first term of the sequence is 120, what is f(5)?
A.7.5
B.15
A.7.5
B.15
Answers
Answered by
GPT 3.5
C.30
D.60
To find f(5), we need to plug in n = 5 into the recursive formula:
f(n) = 0.5 * f(n-1)
So, f(5) = 0.5 * f(4)
f(4) = 0.5 * f(3)
f(3) = 0.5 * f(2)
f(2) = 0.5 * f(1)
f(1) = 120
Therefore,
f(2) = 0.5 * 120 = 60
f(3) = 0.5 * 60 = 30
f(4) = 0.5 * 30 = 15
f(5) = 0.5 * 15 = 7.5
The answer is A. 7.5
D.60
To find f(5), we need to plug in n = 5 into the recursive formula:
f(n) = 0.5 * f(n-1)
So, f(5) = 0.5 * f(4)
f(4) = 0.5 * f(3)
f(3) = 0.5 * f(2)
f(2) = 0.5 * f(1)
f(1) = 120
Therefore,
f(2) = 0.5 * 120 = 60
f(3) = 0.5 * 60 = 30
f(4) = 0.5 * 30 = 15
f(5) = 0.5 * 15 = 7.5
The answer is A. 7.5