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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.
A certain arithmetic sequence has the recursive formula If the common difference between the terms of the sequence is -11 what term follows the term that has the value 11?
In this case, 22 would have the value of 11.
What is the first five terms of two different sequences in which twelve is the 3rd term?
10,11,12,13,14 or 8,10,12,14,16
Why 5x2y and 3xy2 are NOT like terms?
The powers of x in the two terms are different.The powers of x in the two terms are different.The powers of x in the two terms are different.The powers of x in the two terms are different.
What are the first four terms of the geometric sequence with a t1 equals 3 and tn equals 2tn-1?
Assuming the recursive definition is tn = 2*tn-1 t1 = 3 t2 = 2*t1 = 2*3 = 6 t3 = 2*t2 = 2*6 = 12 t4 = 2*t3 = 2*12 = 24
Are all patterns recursive?
No, patterns with terms that are not based upon previous terms are not recursive. Example: i * i where i is the nth term of the pattern.
What is the recursive patterns for 4 and 7 as the first 2 terms?
To establish a recursive pattern starting with 4 and 7 as the first two terms, we can define the sequence such that each subsequent term is the sum of the previous two terms. Thus, the recursive formula would be ( a_n = a_{n-1} + a_{n-2} ) with initial conditions ( a_1 = 4 ) and ( a_2 = 7 ). The next terms would be ( a_3 = 4 + 7 = 11 ), ( a_4 = 7 + 11 = 18 ), and so on. This creates a sequence: 4, 7, 11, 18, ...
How many recursive patterns can you find with 4 plus 7 as the first 2 terms?
Infinitely many. For example: Un+1 = Un + 3 or Un+1 = 2*Un - 1 or Un+1 = 3*Un - 5 or, more generally, Un+1 = k*Un + 7 - 4*k where k is any number. Each one of them will be different from the third term onwards. These are linear patterns. There are quadratic and other recursive relationships.
How do you find a recursive equation?
To find a recursive equation, start by identifying the relationship between consecutive terms in a sequence. Define the first term(s) explicitly, then express each subsequent term as a function of one or more previous terms. Analyze patterns in the sequence to formulate a general rule that captures the relationship. Finally, verify the equation by checking if it holds true for the initial terms of the sequence.
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, ...
Why is Fibonacci recursive?
Each term, except the first two, in the Fibonacci sequence is defined in terms of terms that went earlier in the sequence. That is the meaning of "recursive". t(1) = 1 t(2) = 1 t(n+2) = t(n) + t(n+1) for n = 1, 2, 3, ...
How are recursive and explicit rules the same?
Recursive and explicit rules are both methods used to define sequences in mathematics. They both provide a way to generate terms of a sequence, where a recursive rule defines each term based on previous terms, while an explicit rule provides a formula to calculate any term directly. Despite their different approaches, both types of rules ultimately serve the same purpose: to describe the pattern or relationship within a sequence. Additionally, both can be used to analyze and predict future terms in the sequence.
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 difference between a explicit equation and a recursive equation?
An explicit equation defines a sequence by providing a direct formula to calculate the nth term without needing the previous terms, such as ( a_n = 2n + 3 ). In contrast, a recursive equation defines a sequence by specifying the first term and providing a rule to find subsequent terms based on previous ones, such as ( a_n = a_{n-1} + 5 ) with an initial condition. Essentially, explicit equations allow for direct access to any term, while recursive equations depend on prior terms for computation.
What is a base case?
A base case is the part of a recursive definition or algorithm which is not defined in terms of itself.
What is base case?
A base case is the part of a recursive definition or algorithm which is not defined in terms of itself.
What describes a recursive sequence A a sequence that has a common difference between terms B a sequence that has a common ratio between terms C a sequence relating a term to one?
A: Un+1 = Un + d is recursive with common difference d.B: Un+1 = Un * r is recursive with common ratio r.C: The definition seems incomplete.A: Un+1 = Un + d is recursive with common difference d.B: Un+1 = Un * r is recursive with common ratio r.C: The definition seems incomplete.A: Un+1 = Un + d is recursive with common difference d.B: Un+1 = Un * r is recursive with common ratio r.C: The definition seems incomplete.A: Un+1 = Un + d is recursive with common difference d.B: Un+1 = Un * r is recursive with common ratio r.C: The definition seems incomplete.
