Logic behind numeric sequence

Question

There was this sequence on a magazine and the reader has to find the next number:

10, 2, 4, 6, 2, 8

I couldn't find one, then I found the answer in the next magazine. They say the number is 5, so the sequence is

10, 2, 4, 6, 2, 8, 5

Now I know the answer, but I can't find the logic behind it.

Why is this the answer?

Answer 1

Are we sure the following number is $5$, and not :

$2$ ?

Because :

It could be three nested sequences :
$A = 10, 6, 2, ...$ or $a_n = a_{n-1} - 4$ with $a_0 = 10 $
$B = 2, 2, 2, ...$ or $b_n = 2, \forall n$
$C = 4, 8, 12, ...$ or $c_n = c_{n-1} + 4$ with $c_0 = 4 $

The sequence would be:

$a_0 = 10, b_0 = 2, c_0 = 4, a_1 = 6, b_1 = 2, c_1 = 8$

Then, the following numbers would be :

$a_2 = 2, b_2 = 2, c_2 = 12$

Or :

I can be utterly wrong and this is more lateral-thinking than I thought!

Answer 2

I tried it! Might be the correct answer or a vague logic

10,2,4,6,2,8

10,2 On dividing 10 from x leaves remainder 2 Min Number: 4

10,2,4 On dividing 10 from x leaves remainder 4 Min Number 6

10,2,4,6 On dividing 10 from x leaves remainder 6

Some smartness here, modified the clause

On dividing 102 from x leaves remainder 6 Min Number 12

10,2,4,6,2 (because 12 => 2)

On dividing 102 from x leaves remainder 12 Min number 18

10,2,4,6,2,8

Quotient in this case was 5

So may be that is why answer is 5.

Answer 3

10, 2, 4, 6, 8, 5

10 / 2 = 5, the end number is the common multiple of the previous number divided by the initial number

The common multiple becomes the second number

The common multiple is added to the second number 3 times to make the following three numbers in sequence

Then topped off by the 5 resulted from the common multiple divided from the initial.