anonymous
  • anonymous
Find the first four terms of a squence using the recursive definition. f(1)=6, f(n)=f(n-1)-5
Algebra
chestercat
  • chestercat
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amistre64
  • amistre64
what does the definition tell us?
anonymous
  • anonymous
Using a process that can be repeated. So like the arithmetic sequence. The arithmetic sequence is adding a constant of the previous term.
amistre64
  • amistre64
ok, in this case, what are we 'adding' to one term to make the next term? any ideas?

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amistre64
  • amistre64
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
amistre64
  • amistre64
so, what would our 4 terms be?
anonymous
  • anonymous
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.
amistre64
  • amistre64
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) ?
amistre64
  • amistre64
as we find each new term, we can use it to find the next one .... hence the naming it: 'recursive'
amistre64
  • amistre64
f(4) = f(4-1) - 5 f(4) = f(3) - 5 ^^^ but we know f(3) = -1 f(4) = -1 - 5
amistre64
  • amistre64
pfft, f(3) = -4 .... these tired old eyes play tricks on me
amistre64
  • amistre64
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
anonymous
  • anonymous
Oka, I understand but im confused on f(4)
amistre64
  • amistre64
ok, tell me how you are looking at f(4) show me your working
amistre64
  • amistre64
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.
anonymous
  • anonymous
So f(4)=-6?
amistre64
  • amistre64
f(4) = f(3) - 5 f(3) = -4 [i mistyped it before as -1] f(4) = -4 -5
amistre64
  • amistre64
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
anonymous
  • anonymous
So f(4)=-9
amistre64
  • amistre64
yes
amistre64
  • amistre64
now, what are our 4 terms?
anonymous
  • anonymous
1,-5,-4,-9
amistre64
  • amistre64
f(1) = 6 f(2) = 6-5 = 1 f(3) = 6-5-5 = -4 f(4) = 6-5-5-5 = -9
anonymous
  • anonymous
oh im sorry I didnt mean to write -5 but thank you so much
amistre64
  • amistre64
\[\begin{pmatrix}n\\f(n)\end{pmatrix}=\begin{pmatrix}1&2&3&4\\6&1&-4&-5\end{pmatrix}\]
amistre64
  • amistre64
good luck :)
amistre64
  • amistre64
yeah, 6, 1 -4, -9 math and typing dont mix that well
anonymous
  • anonymous
I agree on that ,Do you think you can help me with a couple more?
amistre64
  • amistre64
maybe one more; its late (1235) and work comes early in the morning
anonymous
  • anonymous
Okay thank you. f(1)=2,f(n)=-3f(n-1)+[f(n-1)]^2
amistre64
  • amistre64
well this ones just a exercise in plugging in the value ... show me your work for n=2
amistre64
  • amistre64
dunno if it helps any to rewrite it by factoring: f(n) = f(n-1) [f(n-1) -3] your call
anonymous
  • anonymous
Wait okay so do I plug 2 in for n?
amistre64
  • amistre64
ideally yes, since 2 is the number after 1.
anonymous
  • anonymous
Okay so I have f(2)=-3f(2-1)+[f(2-1)]^2
amistre64
  • amistre64
good, and since 2-1 = 1 f(2) = -3 f(1) + [f(1)]^2 and what does f(1) equal?
anonymous
  • anonymous
Im not sure in what to do after
amistre64
  • amistre64
you replace f(1) with what its vale is, and work the math
amistre64
  • amistre64
*value
anonymous
  • anonymous
So would Imultiply -3 by 1? =-3
anonymous
  • anonymous
Or where would I get the value from?
amistre64
  • amistre64
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
anonymous
  • anonymous
Okay thank you so much
amistre64
  • amistre64
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 ....

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