As a sequence, you multiply by 4 and add 1.
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.
43. Alternatively add and subtract, doubling the amount each time, starting with 1: 0 + 1 = 1 1 - 2 = -1 -1 + 4 = 3 3 - 8 = -5 -5 + 16 = 11 11 - 32 = -21 So add 64 for the next term: -21 + 64 = 43 (The next term would then be subtract 128: 43 - 128 = -85)
The next in a pattern or sequence. Consecutive even numbers are 22, 24 and 26. 85, 86 and 87 are consecutive integers.
A Partial Sum is a Sum of Part of a Sequence. You must have a sequence to find the partial sum. The regular sum of 67 + 85 is 152.
As a sequence, you multiply by 4 and add 1.
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.
This is a Fibonacci sequence. Each number in the sequence is the sum of the previous two numbers:3+5=85+8=138+13=2113+21=34
217! I promise.
217
43. Alternatively add and subtract, doubling the amount each time, starting with 1: 0 + 1 = 1 1 - 2 = -1 -1 + 4 = 3 3 - 8 = -5 -5 + 16 = 11 11 - 32 = -21 So add 64 for the next term: -21 + 64 = 43 (The next term would then be subtract 128: 43 - 128 = -85)
The next in a pattern or sequence. Consecutive even numbers are 22, 24 and 26. 85, 86 and 87 are consecutive integers.
The next in a pattern or sequence. Consecutive even numbers are 22, 24 and 26. 85, 86 and 87 are consecutive integers.
2+3=53+5=85+8=1313+21=3333 is the next number in this pattern. This pattern is called a Fibonacci.
A Partial Sum is a Sum of Part of a Sequence. You must have a sequence to find the partial sum. The regular sum of 67 + 85 is 152.
1-7-21-46-85-141. Take the "first differences" between the numbers. 6, 14, 25, 39, 56. Take the SECOND differences. 8, 11, 14, 17. Ah. It looks like a sequence where the second difference is two. Continue the next number in the second difference list. It would be 17 + 3 = 20. Add that number to the last number in the first difference list. 56 + 20 = 76. And that's what you add to the last number in the original pattern to get the next number in it. 141 + 76 = 217.
85