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.
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, ...
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