### Brain Teasers

# A Non-Decimal Series

Series
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.

What is the next term in the following series?

1, 2, 4, 13, 31, 112, 224, ?

1, 2, 4, 13, 31, 112, 224, ?

### Answer

1003These numbers are to the base 5.

Eg: 13 base 5 is 8 in decimals (base 10).

Similarly the others in the series are

Base 5 decimal

31 16

112 32

224 64

Thus the series, in base 10, is:

1, 2, 4, 8, 16, 32, 64

The obvious next term is 128 which, when converted to base 5, gives 1003.

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