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This sequence consists of triplets; each triplet is linked to each other.

$1,36,8,2,48,4,3,60,0,\text{X},\text{X},\text{X}$

The three $\text{X}$'s signify the missing numbers.

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The next triplet is

3,72,6

because

we are counting up in multiples of 6: 18, 24, 30, ... and for each we are splicing twice the number between its two digits.

(Thanks to @NoLand'sMan for pointing out in comments that I can't count.)

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  • $\begingroup$ Did you mean 72 instead of 84? $\endgroup$ – NoLand'sMan May 11 at 4:13
  • $\begingroup$ @NoLand'sMan Duh, of course I do. Will fix. Thanks. $\endgroup$ – Gareth McCaughan May 11 at 10:37
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4 72 -4

because

base on each term relation in the triplet

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  • 2
    $\begingroup$ Please explain exactly what you believe the "relation" to be. $\endgroup$ – Hugh May 11 at 3:29
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Here is another offering.

Arranging the triplets in rows

$1 \space 36 \space 8$
$2 \space 48 \space 4$
$3 \space 60 \space 0$

It can be seen that:
The first column is the row/triplet number so the next is $4$.
The second column is an arithmetic progression so the next is $72$.
The third column is an arithmetic progression but I want to avoid a negative number and duplicating another answer.

So I multiply the first 3 digits in each row and take the modulus of 10.

$1 \space 36 \space (1 \cdot 3 \cdot 6) \equiv 8 \pmod {10}$
$2 \space 48 \space (2 \cdot 4 \cdot 8) \equiv 4 \pmod {10}$
$3 \space 60 \space (3 \cdot 6 \cdot 0) \equiv 0 \pmod {10}$

and then

$4 \space 72 \space (4 \cdot 7 \cdot 2) \equiv 6 \pmod {10}$

So my answer is: $4 \space 72 \space 6$

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