One recursive pattern starting with 4 and 7 could be the Fibonacci-like sequence where each term is the sum of the two preceding ones: 4, 7, 11, 18, 29, and so on. Another pattern could involve alternating addition and subtraction; for example, starting with 4, then adding 3 to get 7, then subtracting 1 to get 6, and repeating this with the results: 4, 7, 6, 9, 8, 11, etc.
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.
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, ...
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, ...).
no it is not a recursive pattern because it isn't equal numbers.
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.
there are 4 different ways you can do it
8/4/2=1
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.
no it is not recursive
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, ...).
It look like a Fibonacci sequence seeded by t1 = 2 and t2 = 1. After that the recursive formula is simply tn+1 = tn-1 + tn.
no it is not a recursive pattern because it isn't equal numbers.
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.
t(1) = 3 t(n) = t(n-1) + 2(n-2) for n = 2, 3, 4, ...
x_n+1 = x_n / 4
t(n+1) = t(n) + 6 t(1) = -14
Becasue the browser used by this site is unable to display most mathematical notation, this may not be the correct recursive formula, but:if a(1) = 2 and a(n) = 4*a(n-1)^2 then then a(2) = 4*2^2 =4*4 =16 and a(3) = 4*4^2 = 4*16 = 64