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kipiarov [429]
2 years ago
12

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)?

Mathematics
2 answers:
swat322 years ago
8 0

Answer:

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 :)

kumpel [21]2 years ago
5 0
<u><em>Answer:</em></u>
f (5) = 7.5

<u><em>Explanation:</em></u>
<u>The function given is:</u>
f (n+1) = -0.5 f (n)

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

<u>We will get the other terms by substitution as follows:</u>
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 :)
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