0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.
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They are a sequence of odd numbers. The next three in the sequence would be 17,19 & 21
The numbers are increasing by 1,4,9,16,25,36.... which are square numbers so the next increase is 49. Making the next number in the sequence 141
22.5, 33.75, 50.625...
Natural numbers only: Sequence length 1: 48. Sequence length 3: 15, 16, 17. If you allow for negative numbers, the following two are also possible: Sequence length 33: -14, -13, ... , 0, 1, ..., 15, 16, 17. Sequence length 97: -47, -46, ..., 47, 48. There is no other sequence with a total of 48 in the whole number domain. A solution would be: Let m be the first consecutive number. Hence: m + 1 = Second consecutive no. m + 2 = Third consecutive no. So the equation will be: 1st no. + 2nd no. + 3rd no = 48 m + (m + 1) + (m + 2) = 48 3m + 3 = 48 3m = 48 - 3 3m = 45 Dividing both sides by 3 gives: m = 15 by substitution: 15 + 1 = Second consecutive no. = 16 15 + 2 = Third consecutive no. = 17 Hence, the numbers are 15, 16 and 17. :-)
The sequence of differences between consecutive numbers is 9, 1, -20, 9, 1. If this continues then the next difference is -20 and therefore the seventh number is -5. (15 - 20).