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What is the Th term of the arithmetic sequence given by the explicit rule?
The answer depends on what the explicit rule is!
How do you do recursive pattern rule?
a recursive pattern is when you always use the next term in the pattern... for example 4,(x2+1) 9,(x2+1) 19,(x2+1) 39,(x2+1) 79,(x2+1) 159
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 is a recursive rule for the following arithmetic sequence 27 24 21 18 15?
U1 = 27 U{n+1} = U{n} - 3
What is the difference between an arithmetic series and an arithmetic sequence?
An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.
What is the recursive rule and explicit rule for 3 12 48?
Each number is -4 times the previous one. That means that you can write a recursive rule as: f(1) = -3 f(n) = -4 * f(n-1) The explicit rule involves powers of -4; you can write it as: f(n) = -3 * (-4)^(n-1)
What is the recursive rule and explicit rule for -3 12 -48 192?
Each number is -4 times the previous one. That means that you can write a recursive rule as: f(1) = -3 f(n) = -4 * f(n-1) The explicit rule involves powers of -4; you can write it as: f(n) = -3 * (-4)^(n-1)
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 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 ).
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.
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.
What is recursive rule?
A recursive rule is one which can be applied over and over again to its own output
What does recursive mean?
Recursive refers to using a rule or procedure that can be applied repeatedly.
What are the advantages and disadvantages of a recursive rule compared to an explicit rule?
Recursive rules define a sequence based on previous terms, making them useful for generating terms step-by-step, which can be intuitive for understanding relationships in sequences. However, they can be less efficient for calculating specific terms, especially for large indices, as they may require multiple calculations. In contrast, explicit rules provide a direct formula for finding any term in the sequence, allowing for quicker calculations. The disadvantage of explicit rules is that they may be more complex to derive and less intuitive for understanding the sequence's progression.
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.
What is the Th term of the arithmetic sequence given by the explicit rule?
The answer depends on what the explicit rule is!
What is the difference between a variable and a rule?
a variable changes a rule doesn't.
