What consecutive numbers total 48?

Answer 1

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. :-)