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Recurrence relations and sequences 
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#1
Jul604, 06:58 AM

P: 18

Hi...
1. so can i say that a recurrence relation is a description of the operation(s) involved in a sequence...???... 2. is the formula for an arithmetic sequence, a recurrence relation...???... and is the formula for a geometric sequence, a recurrence relation...???... 


#2
Jul604, 07:12 AM

P: 79

1.Say rather that it is a rule which forms sequence.
2.If you mean [tex]a_{n+1}=a_n+d[/tex], then it is. 3.If you mean [tex]a_{n+1}=qa_n[/tex], then it is. Any form like this: [tex]a_1=x[/tex] [tex]a_{n+1}=f(a_n...a_1)[/tex] is a recurrence relation. 


#3
Jul604, 07:33 AM

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HW Helper
P: 9,398

It needn't be just a function of the previous term in the sequence. that is a first order recurrence relation, for want of a better term (think first order differential equation). things such as the fibonacci numbers satisfy a degree two difference equation (recurrence relation):
a_1=1, a_2=1, a_n=a_{n1}=a_{n2} for n>2, for example 


#4
Jul704, 12:13 PM

P: 18

Recurrence relations and sequences
Hi...thanks...
i was told that a recurrence relation expresses a term in the sequence with regards to other terms in the sequence...whereas the formulae for the arithmetic and geometric sequences don't... ...???... 


#5
Jul704, 12:53 PM

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PF Gold
P: 11,155

[tex] a_n = a_{n1} + d,~~ n = 1,2,3,... [/tex] This is how an AS is defined. But it's not hard to figure from here, that [tex] a_n = a_1 + (n1)d , ~~for~~ n=1,2,3,...[/tex] 


#6
Jul704, 03:05 PM

P: 18

Hi...thanks...
1. so i guess there's a similar recurrence relation for a geometric sequence...???... 2. so then why have a recurrence relation when you can express the SAME sequence by a formula...???... 


#7
Jul704, 03:32 PM

Emeritus
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PF Gold
P: 11,155

[tex]a_n=r*a_{n1}, ~n=1,2,3,...[/tex] [tex] ~~~ = a_1*r^{n1}[/tex] Sometimes, it hard (or impossible ) to find a formula for the n'th term, but you can describe the entire series by a recurrence relation. For the Fibonacci Sequence (decribed by matt, above) it's hard to find such a formula (though there is a good approximation that works well for the large terms ). 


#8
Jul704, 04:20 PM

P: 1,370




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