Question

A sequence is defined recursively using the formula f(n+1)=-0.5f(n). If the first term of the sequence is 120, what is f(5)?

Answer 1

the answer is -15.

Step-by-step explanation:

We know f(1)=120 so from that information we can solve the rest of the equation.

f(1) = 120

f(1+1) = -0.5f(120)

f(2) = -60

f(2+1) = -0.5f(-60)

f(3) = 30

f(3+1) = -0.5f(30)

f(4) = -15

f(4+1) = -0.5f(-15)

f(5)= 7.5

I took the test and got it right but I wanted to explain it for anyone that is having issues with it. Hope this helps :)

Answer 2

Answer:
f (5) = 7.5

Step-by-step explanation:
The function given is:
f (n+1) = -0.5 f (n)

We are also given that:
first term is 120
This means that:
f (1) = 120

We will get the other terms by substitution as follows:
f (2) = -0.5 f (1) = -0.5(120) = -60
f (3) = -0.5 f(2) = -0.5(60) = 30
f (4) = -0.5 f(3) = -0.5(30) = -15
f (5) = -0.5 f(4) = -0.5(-15) = 7.5

Therefore, f (5) = 7.5

Hope this helps :)