Question

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)?

Answer 1

try to find f(2) first
then f(3)
then f(4)
then f(5)
then finally f(6)

Answer 2

find f(2) by replacing the n's with 1
f(n+1)=f(n)-8
f(1+1)=f(1)-8
f(2)=f(1)-8=?

Answer 3

i am not sure how to do that

Answer 4

f(1) is given...

Answer 5

do you see f(1)=100 above?

Answer 6

replace f(1) with 100
so
f(2)=100-8=?

Answer 7

oh that make sense now thanks

Answer 8

now try finding f(3) by replacing the n's with 2 instead

Answer 9

f(3)=182

Answer 10

\[f(n+1)=f(n)-8 \\ \\ \text{ replace } n \text{ with 2 } \\ f(2+1)=f(2)-8 \\ f(3)=f(2)-8 \\ \text{ remember we found } f(2) \text{ to be 92 } \\ f(3)=92-8=?\]

Answer 11

84

Answer 12

you should notice that each time we do these outputs are decreasing by 8 units
we started with f(1)=100
then we got f(2)=92
then we got f(3)=84
so we should get f(4)=?

Answer 13

just keep following the pattern
take 8 away from previous output

Answer 14

ok got it

Answer 15

and f(6) isn't too far away
:p

Answer 16

cool I got f(6)=60