what is the recursive formula for this geometric sequence?
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: 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.
Recursive Form
A sequence usually has a position-to-value function. Alternatively, it can be derived from the recursive relationship that defines the sequence.
what is the recursive formula for this geometric sequence?
-7
4, -1236, -108 is not a geometric system.
It look like a Fibonacci sequence seeded by t1 = 2 and t2 = 1. After that the recursive formula is simply tn+1 = tn-1 + tn.
true
In this case, 22 would have the value of 11.
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.
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
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.
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.
Recursive Form
A sequence usually has a position-to-value function. Alternatively, it can be derived from the recursive relationship that defines the sequence.