Question

Find the first four terms of a squence using the recursive definition.
f(1)=6, f(n)=f(n-1)-5

Answer 1

what does the definition tell us?

Answer 2

Using a process that can be repeated. So like the arithmetic sequence. The arithmetic sequence is adding a constant of the previous term.

Answer 3

ok, in this case, what are we 'adding' to one term to make the next term? any ideas?

Answer 4

or if we simply let n={1,2,3,4} and the rule defined, we get:

f(1) = 6
f(2) = f(1) -5
f(3) = f(2) -5
f(4) = f(3) -5

Answer 5

so, what would our 4 terms be?

Answer 6

So since its asking for the first four terms wouldnt it be f(1)=6
f(n)=f(n-1)-5
f(2)=f(2-1)-5=f(1)+1= 6+1=7 so 7 would be one of the four terms but I dont know how to get the rest.

Answer 7

f(2) = f(2-1) - 5

f(2) = f(1) - 5

f(2) = 6 - 5 = 1, not 7

so, f(1) = 6, f(2) = 1
----------------------

now repeat with n=3

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

f(3) = f(2) - 5

f(3) = 1 - 5 = -4

so, f(1) = 6, f(2) = 1, f(3) = -4

what is f(4) ?

Answer 8

as we find each new term, we can use it to find the next one .... hence the naming it: 'recursive'

Answer 9

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

f(4) = f(3) - 5
^^^
but we know f(3) = -1

f(4) = -1 - 5

Answer 10

pfft, f(3) = -4 .... these tired old eyes play tricks on me

Answer 11

can you tell me how we are working this? its basic to me so i cant really see the difficulty. you have to tell me what it is that is confusing you

Answer 12

Oka, I understand but im confused on f(4)

Answer 13

ok, tell me how you are looking at f(4) show me your working

Answer 14

if you know how to get from f(1) to f(2), then the process does not change. f(2) allows us to get f(3), and f(3) allows us to get f(4).

typing errors aside, its pretty repetitive.

Answer 15

So f(4)=-6?

Answer 16

f(4) = f(3) - 5

f(3) = -4 [i mistyped it before as -1]

f(4) = -4 -5

Answer 17

another way to look at it, just subtract 5 from the setup before ...

f(1) = 6

f(2) = 6-5

f(3) = 6-5-5

f(4) = 6-5-5-5

Answer 18

So f(4)=-9

Answer 19

yes

Answer 20

now, what are our 4 terms?

Answer 21

1,-5,-4,-9

Answer 22

f(1) = 6

f(2) = 6-5 = 1

f(3) = 6-5-5 = -4

f(4) = 6-5-5-5 = -9

Answer 23

oh im sorry I didnt mean to write -5 but thank you so much

Answer 24

\[\begin{pmatrix}n\\f(n)\end{pmatrix}=\begin{pmatrix}1&2&3&4\\6&1&-4&-5\end{pmatrix}\]

Answer 25

good luck :)

Answer 26

yeah, 6, 1 -4, -9

math and typing dont mix that well

Answer 27

I agree on that ,Do you think you can help me with a couple more?

Answer 28

maybe one more; its late (1235) and work comes early in the morning

Answer 29

Okay thank you. f(1)=2,f(n)=-3f(n-1)+[f(n-1)]^2

Answer 30

well this ones just a exercise in plugging in the value ...

show me your work for n=2

Answer 31

dunno if it helps any to rewrite it by factoring:

f(n) = f(n-1) [f(n-1) -3]

your call

Answer 32

Wait okay so do I plug 2 in for n?

Answer 33

ideally yes, since 2 is the number after 1.

Answer 34

Okay so I have f(2)=-3f(2-1)+[f(2-1)]^2

Answer 35

good, and since 2-1 = 1

f(2) = -3 f(1) + [f(1)]^2

and what does f(1) equal?

Answer 36

Im not sure in what to do after

Answer 37

you replace f(1) with what its vale is, and work the math

Answer 38

*value

Answer 39

So would Imultiply -3 by 1? =-3

Answer 40

Or where would I get the value from?

Answer 41

f(1) has been defined for you already in your setup

f(1)=2 <------

f(n)=-3f(n-1)+[f(n-1)]^2
-----------------

f(2) = -3 f(1) + [f(1)]^2

f(2) = -3(2) + 2^2 = -6+4 = -2

f(2) = -2
------------------

we know f(2) now, so let n=3 and work the process again

Answer 42

Okay thank you so much

Answer 43

youre welcome .... once we know a new term, we can use it to find the next new term

f(3) = -3 f(2) + [f(2)]^2

f(3) = -3(-2) + [-2]^2 = 6+4

f(3) = 10
----------------

f(4) = -3 f(3) + [f(3)]^2

f(4) = -3(10) + 10^2 = 100-30

etc ....