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.

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.

Sources:

  1. mathguide.com

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