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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.
xn=x1+(n-1)v^t and Pn=P1+(n-1)iP1
Each number is -4 times the previous one. That means that you can write a recursive rule as: f(1) = -3 f(n) = -4 * f(n-1) The explicit rule involves powers of -4; you can write it as: f(n) = -3 * (-4)^(n-1)
Nth number in an arithmetic series equals 'a + nd', where 'a' is the first number, 'n' signifies the Nth number and d is the amount by which each term in the series is incremented. For the 5th term it would be a + 5d
It is not possible to give a conclusive answer because for a recursive relationship of order 1, the first (or 0th) term must be specified.A(n) = (5*n^2 + 3*n + 2*A(1) - 8)/2 for n = 1, 2, 3, ...
-7
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.
recursive rules need the perivius term explicit dont
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.
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
xn=x1+(n-1)v^t and Pn=P1+(n-1)iP1
The answer depends on what the explicit rule is!
Bram van Leer has written: 'Multidimensional explicit difference schemes for hyperbolic conservation laws' -- subject(s): Differential equations, Hyperbolic, Hyperbolic Differential equations
Each number is -4 times the previous one. That means that you can write a recursive rule as: f(1) = -3 f(n) = -4 * f(n-1) The explicit rule involves powers of -4; you can write it as: f(n) = -3 * (-4)^(n-1)
Each number is -4 times the previous one. That means that you can write a recursive rule as: f(1) = -3 f(n) = -4 * f(n-1) The explicit rule involves powers of -4; you can write it as: f(n) = -3 * (-4)^(n-1)
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
explicit is clearly stated and implicit is not clearly stated