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
An explicit equation defines a sequence by providing a direct formula to calculate the nth term without needing the previous terms, such as ( a_n = 2n + 3 ). In contrast, a recursive equation defines a sequence by specifying the first term and providing a rule to find subsequent terms based on previous ones, such as ( a_n = a_{n-1} + 5 ) with an initial condition. Essentially, explicit equations allow for direct access to any term, while recursive equations depend on prior terms for computation.
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