It is a formula, used in sequences, in which the value of the nth term is described in relation to one or more of the earlier terms.
A classic example is the Fibonacci sequence:
u(1) = 1
u(2) = 1
u(n) = u(n-1) + u(n-2) for n = 3, 4, 5, ...
what is the recursive formula for this geometric sequence?
It is often possible to find an explicit formula that gives the same answer as a given recursive formula - and vice versa. I don't think you can always find an explicit formula that gives the same answer.
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.
That sounds like the definition for Recursive Formula.
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.
what is the recursive formula for this geometric sequence?
It is often possible to find an explicit formula that gives the same answer as a given recursive formula - and vice versa. I don't think you can always find an explicit formula that gives the same answer.
The recursive formula for the function f(n) is f(n) f(n/2).
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.
x_n+1 = x_n / 4
A recursive formula is one that references itself. The famous example is the Fibonacci function: fib(n) := fib(n-1) + fib(n-2), with the terminating proviso that fib(0) = 0 and fib(1) = 1.
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.
That sounds like the definition for Recursive Formula.
4, -1236, -108 is not a geometric system.
-7
a recursive association - as a aggregation is a special form of association, so recursive aggregation can be called as recursive association ... AKASH SISODIYA ......IT ...
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.