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 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.
The explicit formula for an arithmetic sequence is given by an = a1 + (n-1)d, where a1 is the first term and d is the common difference. In this case, the first term a1 is 16, and the common difference d is 4. Therefore, the explicit formula for the arithmetic sequence is an = 16 + 4(n-1) = 4n + 12.
In a Fibonacci sequence, sum of two successive terms gives the third term.... here is the Fibonacci sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144........ General formula to generate a Fibonacci sequence is """Fn= Fn-1 + Fn-2""" To check whether a number is Fibonacci or not follow the following steps: 1) Get the number as input from user. 2) Fix the first two numbers of sequence as 0 and 1. 3) put a sentinel loop with upper limit being the input number. 4)in the body of loop generate the next number in sequence in each iteration and continue swapping the values as follows: a=0 b=1 next=a+b while (next< input) a=b b=next next=a+b wend 5) lastly when program exits the loop compare the last number of sequence with the input number if they are equal then number is Fibonacci otherwise not. otherwise the last term of sequence will be less than the input number.