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There are two major problems in answering this question.

The first problem is that there are infinitely polynomials of order 7 that will give these as the first seven numbers and any one of these could be "the" rule. There are also 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 second problem is that you have not specified where, in the sequence the missing number should have been.

If the missing number was the last, the simplest polynomial rule of order 6 ist(n) = (-36*n^6 + 854*n^5 - 7945*n^4 + 36680*n^3 - 87299*n^2 + 99386*n - 39600)/120 for n = 1, 2, 3, ... and, accordingly the next number is -396.

If missing number was the first, the simplest polynomial rule of order 6 is different and the first number is 330.

Q: What is the missing number in this sequence 17 11 8 15 4 10 13?

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The missing number is 5. They're the first five prime numbers.

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If the question is, What is the missing number in the sequence 7, 11, 23, ?, 167? Then each number is 3 times the previous number then deduct 10. 3 x 7 = 21 - 10 = 11 3 x 11= 33 - 10 = 23 3 x 23 = 69 - 10 = 59......the missing number 3 x 59 = 177 - 10 = 167 3 x 167 = 501 - 10 = 491....the next number in the sequence.

The answer depends on where, within the sequence, the missing number should have been.

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The missing number is 5. They're the first five prime numbers.

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It all depends on the sequence you are talking about. For example, the next number in the sequence 0,1,1,2,3,5,8,13,_ would be 21. This would be the Fibonacci sequence as the rule is add the 2 previous terms to get the next term. Another example would be this: 11,121,1331,14641,______.The missing number is 161051, following the pattern of powers of 11, 11^1, 11^2, 11^3 and so on. If you understand what I am trying to say, it all depends on the sequence you are trying to find the number in.

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That would be -5.