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Starting with the numbers 4 and 7, you can create the following recursive patterns:
- Addition Pattern: Each term is the sum of the previous two terms, starting with 4 and 7 (e.g., 4, 7, 11, 18, 29, ...).
- Multiplication Pattern: Multiply the previous two terms to get the next one (e.g., 4, 7, 28, 196, ...).
- Alternating Addition/Subtraction Pattern: Alternate adding and subtracting the original numbers (e.g., 4, 7, 3, 10, 6, ...).
- Doubling Pattern: Start with 4, then double it, followed by adding 7 to the previous term (e.g., 4, 8, 15, 30, ...).
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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.
Is 1-4-9-16-25-36 a recursive pattern?
no it is not a recursive pattern because it isn't equal numbers.
Is 1 4 9 16 25 36 a recursive pattern?
Yes
What is the recursive formula for 1 4 13 40 121?
The sequence 1, 4, 13, 40, 121 can be described by a recursive formula. The recursive relationship can be expressed as ( a_n = 3a_{n-1} + 1 ) for ( n \geq 2 ), with the initial condition ( a_1 = 1 ). This means each term is generated by multiplying the previous term by 3 and then adding 1.
What is a recursive formula and what is it used for Geometric and Arithmetic?
A recursive definition is any definition that uses the thing to be defined as part of the definition. A recursive formula, or function, is a related formula or function. A recursive function uses the function itself in the definition. For example: The factorial function, written n!, is defined as the product of all the numbers, from 1 to the number (in this case "n"). For example, the factorial of 4, written 4!, is equal to 1 x 2 x 3 x 4. This can also be defined as follows: 0! = 1 For any "n" > 0, n! = n x (n-1)! For example, according to this definition, the factorial of 4 is the same as 4 times the factorial of 3. Try it out - apply the recursive formula, until you get to the base case. Note that a base case is necessary; otherwise, the recursion would never end.
