If f(1)=8 and f(n)=1/4f(n-1) what are the first five terms of this sequence?

Answer 1

8, 2, 1/2, 1/8, 1/32

Answer 2

Starting out, they've actually given us the first term! f(1) = 8 means our first term is 8. Now we need to find f(2) for our second term. To do this we will plug 2 in for n.

f(2) = 1/4 * f(2-1)

f(2) = 1/4 * f(1)

Now, we know f(1) = 8, so we can plug 8 in for f(1)

f(2) = 1/4 * (8)

f(2) = 2

So our second term is 2! Now we repeat the process for terms 3,4, and 5:

f(3) = 1/4 * f(3-1)

f(3) = 1/4 * f(2)------->f(2) = 2

f(3) = 1/4 * 2

f(3) = 1/2

f(4) = 1/4 * f(4-1)

f(4) = 1/4 * f(3)------->f(3) = 1/2

f(4) = 1/4 * 1/2

f(4) = 1/8

f(5) = 1/4 * f(5-1)

f(5) = 1/4 * f(4) ------> f(4) = 1/8

f(5) = 1/4 * 1/8

f(5) = 1/32

So our first five terms are 8, 2, 1/2, 1/8, and 1/32. I hope this explanation was thorough and answered all of your questions. If you need additional help don't hesitate to reach out! Learn on! :)