Starting with the numbers 4 and 7, you can create the following recursive patterns:
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.
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, ...
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 a recursive pattern because it isn't equal numbers.
Yes
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.
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, ...
there are 4 different ways you can do it
no it is not recursive
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 a recursive pattern because it isn't equal numbers.
8/4/2=1
x_n+1 = x_n / 4
Yes
4, -1236, -108 is not a geometric system.
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.
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)