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What is the recursive rule and explicit rule for 3 7 11 15?
The sequence 3, 7, 11, 15 is an arithmetic sequence where each term increases by 4. The recursive rule can be expressed as ( a_n = a_{n-1} + 4 ) with ( a_1 = 3 ). The explicit rule for the nth term is ( a_n = 3 + 4(n - 1) ) or simplified, ( a_n = 4n - 1 ).
Recursive rule for the Fibonacci sequence?
x1=0 x2=1 for i > 2, xi= xi-1 + xi-2
What is recursive rule?
A recursive rule is one which can be applied over and over again to its own output
Is the explicit rule for a geometric sequence defined by a recursive formula of for which the first term is 23?
Yes, the explicit rule for a geometric sequence can be defined from a recursive formula. If the first term is 23 and the common ratio is ( r ), the explicit formula can be expressed as ( a_n = 23 \cdot r^{(n-1)} ), where ( a_n ) is the nth term of the sequence. This formula allows you to calculate any term in the sequence directly without referencing the previous term.
Why does the explicit rule provide more information about sequences than the recursive rule?
The explicit rule provides a direct formula to calculate any term in a sequence without needing to know the previous terms, allowing for quicker evaluations and a clearer understanding of the sequence's behavior. In contrast, the recursive rule defines each term based on the preceding term, which can be less efficient for finding distant terms and may obscure the overall pattern. This makes the explicit rule particularly useful for analyzing and predicting the long-term behavior of sequences.
What is the difference between an explicit rule and a recursive rule?
An explicit rule defines the terms of a sequence in terms of some independent parameter. A recursive rule defines them in relation to values of the variable at some earlier stage(s) in the sequence.
What is the recursive rule and explicit rule for 3 7 11 15?
The sequence 3, 7, 11, 15 is an arithmetic sequence where each term increases by 4. The recursive rule can be expressed as ( a_n = a_{n-1} + 4 ) with ( a_1 = 3 ). The explicit rule for the nth term is ( a_n = 3 + 4(n - 1) ) or simplified, ( a_n = 4n - 1 ).
Recursive rule for the Fibonacci sequence?
x1=0 x2=1 for i > 2, xi= xi-1 + xi-2
What is recursive rule?
A recursive rule is one which can be applied over and over again to its own output
Do grapes come under Fibonacci sequence?
No. Grapes have nothing to do with a recursive series of numbers following the rule that any number is the sum of the previous two.
What does recursive mean?
Recursive refers to using a rule or procedure that can be applied repeatedly.
What is a recursive rule for the following arithmetic sequence 27 24 21 18 15?
U1 = 27 U{n+1} = U{n} - 3
Is 1 11 20 30 39 a recursive pattern?
Yes. The next two numbers would be 49 & 58. This is because, from the first number, the pattern repeats by adding 10 then 9. So - 39+19 is 49, and 49+9=58.
What is a recursive rule?
It is a term for sequences in which a finite number of terms are defined explicitly and then all subsequent terms are defined by the preceding terms. The best known example is probably the Fibonacci sequence in which the first two terms are defined explicitly and after that the definition is recursive: x1 = 1 x2 = 1 xn = xn-1 + xn-2 for n = 3, 4, ...
How is the recursive form of a sequence sometimes more useful than the closed form where a rule is found to find any term based on its position in the sequence?
"The recursive form is very useful when there aren't too many terms in the sequence. For instance, it would be fairly easy to find the 5th term of a sequence recursively, but the closed form might be better for the 100th term. On the other hand, finding the closed form can be very difficult, depending on the sequence. With computers or graphing calculators, the 100th term can be found quickly recursively."
How do you get a recursive pattern?
A recursive pattern is a pattern that goes like this 2,4,6,8 and on. A pattern rule which is used to find the next term.
How do you find a recursive rule?
You can search on ebay or more likey to find at Staples :)
