A) an=an-1 -13.8
B) an=an -1+13.8
C) an=an+1+13.8
D)an=an+1-13.8
x1=0 x2=1 for i > 2, xi= xi-1 + xi-2
A recursive rule is one which can be applied over and over again to its own output
"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."
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Anything you like. You specify whatever rule you like and the resulting set of numbers is the sequence based on that rule.
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.
x1=0 x2=1 for i > 2, xi= xi-1 + xi-2
A recursive rule is one which can be applied over and over again to its own output
No. Grapes have nothing to do with a recursive series of numbers following the rule that any number is the sum of the previous two.
Recursive refers to using a rule or procedure that can be applied repeatedly.
U1 = 27 U{n+1} = U{n} - 3
It is a term for sequences in which a finite number of terms are defined explicitly and then all subsequent terms are defined by the preceding terms. The best known example is probably the Fibonacci sequence in which the first two terms are defined explicitly and after that the definition is recursive: x1 = 1 x2 = 1 xn = xn-1 + xn-2 for n = 3, 4, ...
"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."
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.
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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)
Anything you like. You specify whatever rule you like and the resulting set of numbers is the sequence based on that rule.