# Find the next three terms in the sequence

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.

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.)

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

4 72 -4

because

base on each term relation in the triplet

• Please explain exactly what you believe the "relation" to be. – Hugh May 11 at 3:29

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: $$4 \space 72 \space 6$$