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21. This is the Fibonacci series.
The next series in the pattern would start at 102 + 666. the pattern is +6, +66, and, presumably, +666. If the pattern were to hold true and continue it should be 768, 769, 770, 771, 772, 773, 774 that is a total of 6 numbers before the next series in the pattern and then 774 + 6666 for 4 numbers... the sequence for the pattern is 2, 5, 3, 6, 4, 7,...
The next number has to be 41; you always add the powers of three to the previous number beginning with 0. 3^0=1; 1+1=2; 3^1=3; 2+3=5; 3^2=9; 5+9=14; 3^3=27; 14+27=41 the next number would be 122 (81+41); you could also multiply the number by 3 and then substract 1. By the way: x(n)=x(n-1)+3^(x-2) ------------------------------------------------------------------------------------------------------------------- It could also be the Catalan number sequence, found by 1/(n+1) * (2n choose n), in which case the next number would be 42.
The definition of mode regarding to maths is basically a number that appears most in a series of numbers for example 2,3,6,3,2,3 the mode number would be 3 because there is three 3 two 2 and one 6.
The next number is -21
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The series seems to be "add 3," so the next number in the series would be 12 followed by 15.
1Another AnswerEach number of the series appears to double as the series progresses: 1/12 (x2), 1/6 (x2), 1/3 (x2), 2/3, etc. This being so, the next number in the series would be 4/3 or 1-1/3 (2/3 x 2)..
If you look at this series, you can see that each number is 2/3 of the one before it. The next number then is 2/3 * 32, which equals 64/3, or 21 1/3.
The number that comes next in the series 1 2 2 5 3 10 is 7. You get this number by subtracting the number 3 from the number 10.
The next number in the series 3, 618, 72, is -1635. The relevant rule is Un = (-1161n2 + 4713n - 3546)/2 for n = 1, 2, 3, ...
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