what is the recursive formula for this geometric sequence?
The sequence 1, 4, 13, 40, 121 can be described by a recursive formula. The recursive relationship can be expressed as ( a_n = 3a_{n-1} + 1 ) for ( n \geq 2 ), with the initial condition ( a_1 = 1 ). This means each term is generated by multiplying the previous term by 3 and then adding 1.
The recursive formula for a sequence typically defines each term based on previous terms. For a sequence denoted as ( A(n) ), ( B(n) ), and ( C(n) ), a common recursive approach might be: ( A(n) = A(n-1) + B(n-1) ) ( B(n) = B(n-1) + C(n-1) ) ( C(n) = C(n-1) + A(n-1) ) These formulas assume initial values are provided for ( A(0) ), ( B(0) ), and ( C(0) ). Adjustments can be made based on the specific context or properties of the 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.
To find the 20th term of a sequence, first identify the pattern or formula that defines the sequence. This could be an arithmetic sequence, where each term increases by a constant difference, or a geometric sequence, where each term is multiplied by a constant factor. Once the formula is established, substitute 20 into the formula to calculate the 20th term. If the sequence is defined recursively, apply the recursive relation to compute the 20th term based on the previous terms.
what is the recursive formula for this geometric sequence?
4, -1236, -108 is not a geometric system.
-7
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.
The sequence 1, 4, 13, 40, 121 can be described by a recursive formula. The recursive relationship can be expressed as ( a_n = 3a_{n-1} + 1 ) for ( n \geq 2 ), with the initial condition ( a_1 = 1 ). This means each term is generated by multiplying the previous term by 3 and then adding 1.
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