Question

The first four terms of a sequence are shown below:

8, 5, 2, -1

Which of the following functions best defines this sequence?

f(1) = 8, f(n + 1) = f(n) + 3; for n 1
f(1) = 8, f(n + 1) = f(n) - 5; for n 1
f(1) = 8, f(n + 1) = f(n) + 5; for n 1
f(1) = 8, f(n + 1) = f(n) - 3; for n 1

Answer 1

first of all do you have a common difference?

Answer 2

5-8=?
2-5=?
-1-2=?

Answer 3

nevermind
didn't know the answer choices

Answer 4

but you could have set this up as
a(n)=8+(-3)(n-1)

Answer 5

anyways...recursion

Answer 6

\[f(n+1)=f(n)+3\]
replace n with 1

Answer 7

\[f(1+1)=f(1)+3\]

Answer 8

\[f(2)=f(1)+3\]
we are given f(1)=8
so f(2)=?

Answer 9

we are trying the first choice to see what happens
we are trying to see if it's terms match up with the terms given

Answer 10

6

Answer 11

f(2)=f(1)+3
f(2)=8+3
f(2)=11
this first choice will not work
because our second term was suppose to be 5 correct?

Answer 12

we know then that this f(1)+positive number will not work
the numbers are suppose to decrease

Answer 13

check out one of the choices with a minus sign

Answer 14

B and D

Answer 15

it is definitely one of those

Answer 16

the other two sequences will give us an increasing sequence

Answer 17

and we have a decreasing one

Answer 18

f(1)-5=?
f(1)-3=?

Answer 19

which one will give us the correct second term

Answer 20

f1 was 8 correct? so..

8-5 = 3

8-3 = 5

Answer 21

yep

Answer 22

so is 3 our second or is 5?

Answer 23

D

Answer 24

8, 5, 2, -1

so last option is the correct choice :)
yep
f(1)=8
f(2)=8-3=5
f(3)=5-3=2
f(4)=2-3=-1
and so on...

Answer 25

I have another question

Answer 26

ok

Answer 27

the slope for this

Answer 28

slope=rise/run right?

Answer 29

rise is positive if you rise up
rise is negative if you rise down
-
run is positive if you go right
run is negative if you go left

Answer 30

yes

Answer 31

so let's count from Y to X

Answer 32

let's count up from Y

Answer 33

like one sec i will drae

Answer 34

look at that vertical line segment I drew