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.
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.
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because you add the first 2 terms and the next tern was the the sum of the first 2 terms.
"The recursive form is very useful when there aren't too many terms in the sequence. For instance, it would be fairly easy to find the 5th term of a sequence recursively, but the closed form might be better for the 100th term. On the other hand, finding the closed form can be very difficult, depending on the sequence. With computers or graphing calculators, the 100th term can be found quickly recursively."
Suppose Pk is the product of the first k numbers. P1 = 1 Pn = n*Pn-1 for n > 1 Curiously, though, when used for permutations or combinations (or for the Gamma function), P0 = Factorial(0) = 1
there are 4 different ways you can do it
If you cannot find any iterative algorithm for the problem, you have to settle for a recursive one.
A recursive pattern is a pattern that goes like this 2,4,6,8 and on. A pattern rule which is used to find the next term.
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.
You can search on ebay or more likey to find at Staples :)
write a java program to find factorial using recursive and non recursive
Yes, this can be done. For example for Fibonacci series. You will find plenty of examples if you google for the types of series you need to be generated.
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-69
recursion is always slower than iteration
Yes. There are many places online to find patterns. You can search for them or you can order them to be delivered right to your door. The first place I would try would be joannefabrics.com
To find the sum of the first 20 terms of an arithmetic progression (AP), we need to first determine the common difference (d) between the terms. Given that the 6th term is 35 and the 13th term is 70, we can calculate d by subtracting the 6th term from the 13th term and dividing by the number of terms between them: (70 - 35) / (13 - 6) = 5. The formula to find the sum of the first n terms of an AP is Sn = n/2 [2a + (n-1)d], where a is the first term. Plugging in the values for a (the 1st term), d (common difference), and n (20 terms), we can calculate the sum of the first 20 terms.