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There are infinitely many rules based on polynomials of order 5 or above, as well as non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
The simplest rule, based on a polynomial or order 2 is
Un = n^2 - 1.
But it can also be
Un = (-n^5 + 15n^4 - 85n^3 + 245n^2 - 274n + 100)/20.
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What is nth term for 0 3 8 15 24?
Oh, what a beautiful sequence of numbers you've created! To find the pattern, we can see that each number is increasing by adding consecutive odd numbers. The nth term for this sequence can be found using the formula n^2 + n. Just like painting, sometimes all we need is a little patience and observation to uncover the hidden beauty within patterns.
What is the nth term of the sequence 18 12 6 0 -6?
To find the nth term of a sequence, we first need to identify the pattern or rule that governs the sequence. In this case, the sequence is decreasing by 6 each time. Therefore, the nth term can be represented by the formula: 18 - 6(n-1), where n is the position of the term in the sequence.
Find nth term for sequence 0 5 10 15 20 25 30 35?
The given sequence is an arithmetic sequence with a common difference of 5. To find the nth term of an arithmetic sequence, we use the formula: (a_n = a_1 + (n-1)d), where (a_n) is the nth term, (a_1) is the first term, (n) is the term number, and (d) is the common difference. In this case, the first term (a_1 = 0) and the common difference (d = 5). Therefore, the nth term of the sequence is (a_n = 0 + (n-1)5 = 5n - 5).
What is the nth term for 4 14 24 34?
The given sequence appears to be increasing by 10 each time. To find the nth term, we can use the formula for arithmetic sequences: nth term = first term + (n-1) * common difference. In this case, the first term is 4 and the common difference is 10. Therefore, the nth term for this sequence would be 4 + (n-1) * 10, which simplifies to 10n - 6.
What is the nth term for the sequence 0 4 12 24 40 60?
An = 2(n - 1)2 + 2(n - 1) = 2n(n - 1)
