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.
An explicit rule defines the terms of a sequence in terms of some independent parameter. A recursive rule defines them in relation to values of the variable at some earlier stage(s) in the sequence.
what is the recursive formula for this geometric sequence?
All recursive Languages are recursively enumerable. But not all the recursively enumerable languages are recursive. It is just like NP complete.
Explicit: + fast: known expression for solution at next time level { stability restrictions on t. Implicit: + less restrictive conditions on t { must solve equation to update solution
I will explain in the easiest way the difference between the function and recursive function in C language. Simple Answer is argument of the function is differ but in the recursive function it is same:) Explanation: Function int function(int,int)// function declaration main() { int n; ...... ...... n=function(a,b); } int function(int c,int d) { ...... ...... ...... } recursive Function: int recursive(int,int)// recursive Function declaration main() { int n; ..... ..... ..... ..... n=recursive(a,b); } int recursive(int a,int b) { ..... .... .... .... } Carefully see, In the recursive Function the function arguments are same.
clearly
A: Un+1 = Un + d is recursive with common difference d.B: Un+1 = Un * r is recursive with common ratio r.C: The definition seems incomplete.A: Un+1 = Un + d is recursive with common difference d.B: Un+1 = Un * r is recursive with common ratio r.C: The definition seems incomplete.A: Un+1 = Un + d is recursive with common difference d.B: Un+1 = Un * r is recursive with common ratio r.C: The definition seems incomplete.A: Un+1 = Un + d is recursive with common difference d.B: Un+1 = Un * r is recursive with common ratio r.C: The definition seems incomplete.
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
Expression has no answer. a equation has an answer
A function can map for sets with infinite elements. Recursive variables, being 'algorithms of algorithms', are restricted to finite elements.
explicit is clearly stated and implicit is not clearly stated
Explicit is something precisely and clearly communicated, while implicit is something implied though not directly expressed.