The quartic:
t(n) = -n4 + 12n3 - 44.5n2 - 24.5n + 356 fits the data for n = 1, 2, 3, ...
Putting n = 6 gives t(6) = -97
NB: A more popular version of this question has 129 as the third number.
At each step the number being subtracted is reduced by 9 298 - 89 = 209 209 - 80 = 129 129 - 71 = 58 58 - 62 = -4 -4 - 53 = -57..........which is the next number.
-57. You are taking away 9 less each time.
-57
-57 (each number that is subtracted from the first is 9 different from the previous (i.e. 298-89=209-80=129-71=58-62=-4-53=-57). As you can see, the amounts that are substracted are 89, 80, 71, 62, 53 (all 9 different from the one before it.)
-66 The sequence can be generated by the following quartic: t(n) = (-3n4 + 42n3 - 177n2 - 358n + 2808)/8 for n = 1, 2, 3, ...
At each step the number being subtracted is reduced by 9 298 - 89 = 209 209 - 80 = 129 129 - 71 = 58 58 - 62 = -4 -4 - 53 = -57..........which is the next number.
The difference between one number and the next in the sequence is decreasing by 9 each time. Therefore, the difference between -4 and the next number will be equal to 62 - 9 = 53. The next number is therefore equal to -4 - 53 = -57.
The sequence is formed by subtracting 89 at the first step and then reducing this figure by 9 at each successive step. 298 - 89 = 209 209 - 80 = 129 129 - 71 = 58 58 - 62 = -4 -4 - 53 = -57........this is the next number in the series.
It is a quadratic sequence (order 2) t(n) = (9n2 - 205n + 792)/2 for n = 1, 2, 3, ... and the next number is -57
298 less 209 is 89 209 less 129 is 80 129 less 58 is 71 58 less -4 is 62 The result of each subsequent equation is 9 less than the previous one (89, 80, 71...). The next result is going to be 62-9=53. The first number in each equation above is the same as the second number in the previous equation: 298 less 209 is 89 209 less 129 is 80So, the next equation will be: -4 less X is 53 Therefore, X is the next number in the original sequence, which resolves to: -57
The next number is 1112.
N can have any of four values: 125, 161, 209, and 221. Factors of 125 are 1, 5, 25, and 125. Factors of 161are 1, 7, 23, and 161. Factors of 209 are 1, 11, 19, and 209. Factors of 221 are 1, 13, 17, and 221.
-57
-57. You are taking away 9 less each time.
-57
-57
-57