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
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.
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)
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.
x_n+1 = x_n / 4
8/4/2=1
Yes
4, -1236, -108 is not a geometric system.
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)
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.
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.
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)