Q:

# What is the next number in the series 2, 5, 11, 20, 32, 47?

A:

The next number in the series 2, 5, 11, 20, 32, 47 would be 65. The difference between consecutive numbers in these series are multiples of three.

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To derive this number of the series, it is necessary to elucidate the correlation between these numbers in the series. Consider the difference between the consecutive numbers in the series.

5 - 2 = 3 = 3 x 111 - 5 = 6 = 3 x 220 - 11 = 9 = 3 x 332 - 20 = 12 = 3 x 447 - 32 = 15 = 3 x 5

As seen through the various calculations, the difference between the first two consecutive numbers is 3. Thereafter, the difference between consecutive numbers follows a symmetrical pattern: they are all serial multiples of 3. Thus, the difference between the consecutive number is 3, 6, 9, 12, 15. The next number in the serial list of multiples of 3 is 18. Therefore, to arrive at the next number in the series 2, 5, 11, 20, 32, 47, calculate it as follows:

Let the unknown number be x

x - 47 = 18 x = 18 + 47 x = 65

Thus, the new number in this series 2, 5, 11, 20, 32, 47 is 65.

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