What is the Next Number?
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.
What is the next number in this series?
6, 14, 36, 98, 276, ...
Hint
This is not an obvious series. Summation notation is required to solve this teaser.
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Answer
794
The nth term in the series is given by the sum of x^n for x in the range 1 to 3, i.e. 1^n + 2^n + 3^n.
Thus the first term is 1^1 + 2^1 + 3^1 = 1 + 2 + 3 = 6,
the second term is 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14,
and so on.
The sixth term is then 1^6 + 2^6 + 3^6 = 1 + 64 + 729 = 794.
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