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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?
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
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)
true
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
1, 4, 7, 10, 13, …
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, ...