Good Question! After 6 years of math classes in college, and 30+ years of teaching (during which I took many summer classes) I've never seen an explicit formula for the nth term of the Fibonacci sequence.
Study more math and maybe you can discover the explicit formula that you want.
How to answer with formula
The answer depends on what the explicit rule is!
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In order to answer the question is is necessary to know what the explicit formula was. But, since you have not bothered to provide that information, the answer is .
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How to answer with formula
The answer depends on what the explicit rule is!
The explicit formula for a sequence is a formula that allows you to find the nth term of the sequence directly without having to find all the preceding terms. To find the explicit formula for a sequence, you need to identify the pattern or rule that governs the sequence. This can involve looking at the differences between consecutive terms, the ratios of consecutive terms, or any other mathematical relationship that exists within the sequence. Once you have identified the pattern, you can use it to create a formula that will generate any term in the sequence based on its position (n) in the sequence.
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In order to answer the question is is necessary to know what the explicit formula was. But, since you have not bothered to provide that information, the answer is .
The given sequence can be identified as a geometric sequence where each term is multiplied by a common ratio. To find the explicit formula, we note that each term can be expressed as ( a_n = 3 \times (1.5)^{n-1} ), where ( n ) is the term number starting from 1. Thus, the explicit formula for the sequence is ( a_n = 3 \times (1.5)^{n-1} ).
The sequence you've provided seems to be 3, 1, -1, -3, -5. To find the explicit formula for this sequence, we can observe that it starts at 3 and decreases by 2 for each subsequent term. The explicit formula can be expressed as ( a_n = 3 - 2(n-1) ) for ( n \geq 1 ). Simplifying this gives ( a_n = 5 - 2n ).
The explicit formula here is 5+ 6x. solved at x=25 you get 155
(1/sq rt 5)((1+sq rt 5)/2)n - (1/sq rt 5)((1-sq rt 5)/2)n This is based on the golden ratio (1+sq rt 5)/2) because the ratio of 2 Fibonacci terms approaches the golden ratio as the 2 terms used get larger. IE the ratio ot the 10th term to the 9th term is 55/34 = 1.61765 and the golden ratio is approx. 1.61803. When using this formula if your calculator does not round, you will round to get the appropriate Fibonacci number.
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56
The simplest formula isUn = (-8611*n^2 + 34477*n - 25082)/2 for n = 1, 2, 3.