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
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, ...
a recursive formula is always based on a preceding value and uses A n-1 and the formula must have a start point (an A1) also known as a seed value. unlike recursion, explicit forms can stand alone and you can put any value into the "n" and one answer does not depend on the answer before it. we assume the "n" starts with 1 then 2 then 3 and so on arithmetic sequence: an = a1 + d(n-1) this does not depend on a previous value