As a sequence, you multiply by 4 and add 1.
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As you are multiplying by 4 and then adding 1, the next number is 1365.
Oh, dude, the ratio of 105 to 85 is 21:17. It's like dividing both numbers by their greatest common factor, which in this case is 5. But hey, who's counting, right?
850 is not the greatest common factor of 85 and 10. The person answering the question about the numbers with 850 as the greatest common factor was apparently thinking about the factors of 850 itself, not numbers that would have 850 as their greatest common factor. The greatest common factor of 10 and 85 is 5. The least common multiple of 10 and 85 is 170. The product of 10 and 85 is 850.
Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question followed by your chosen number in the next place. 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.One possible solution, using a polynomial of order 3, isU(n) = 39*n^3 - 210*n^2 + 373*n - 197 for n = 1, 2, 3, 4, 5 which gives U(5) = 1293.
The common denominator of any two or more whole numbers, such as 85 and 51, will always be one (1) because 'common denominator' refers to the denominators of two or more fractions or mixed numbers, not whole numbers. So, a set of whole numbers (x,x) would have to be converted to their fraction equivalents, i.e., x/1, which will always yield a denominator of 1.