Question

A sequence is defined recursively using the formula . If the first term of the sequence is 120, what is f(5)?

−15
−7.5
7.5
15

Answer 1

We apply the recursion four times starting from f(1)=120 (assuming f(n+1)=−(1/2)f(n) or f(n+1)=f(n)/−2):

f(2)=120/−2 = −60
f(3)=−60/−2 = 30
f(4)=30/−2 = −15
f(5)=−15/−2 = 7.5

So f(5) = 7.5.