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.
t(n+1) = t(n) + 6 t(1) = -14
8/4/2=1
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
u1 = 38 un+1 = un - 7.5 (for n = 1, 2, 3, ... )
Both 11 and 22 can be divided by 11. So the answer is 1/2 (one over two)
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.
t(n+1) = t(n) + 6 t(1) = -14
The recursive formula for the function f(n) is f(n) f(n/2).
1) Recursive algorithms 2) Basic Principle 3) Analysis
To find the third term of the sequence defined by the recursive rule ( f(1) = 2 ) and ( f(n) = f(n-1) + 1 ), we first calculate ( f(2) ) using the recursive formula. Since ( f(1) = 2 ), we have ( f(2) = f(1) + 1 = 2 + 1 = 3 ). Next, we calculate ( f(3) ) as ( f(3) = f(2) + 1 = 3 + 1 = 4 ). Thus, the third term of the sequence is ( f(3) = 4 ).
8/4/2=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.
1+1=11*100
Oh honey, that's not a recursive pattern, that's just a sequence of numbers increasing by 10 each time. It's like counting by tens but starting at 1 instead of 10. So, no recursion here, just some basic addition.
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
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, ...