please solve this number pattern for me. 4; 3/4; 4; 1/4; 1/12. and find the next two terms

Question

If the pattern continues in the same way, write down the next two terms

Answer 1

4, 3/4, 4, 1/4, 1/12, 4, 1/36, 1/108, 1/324, 4, ... The next two terms are shown in green.

My guess is that the number 4 is in the positions a₁, a₃, a₆, a₁₀, a₁₅, ... progressively moving further apart.

(Note that 1, 3, 6, 10, 15 also form a progression, being the sums of the natural numbers:

1, 1+2, 1+2+3, 1+2+3+4, 1+2+3+4+5, ...)

The intervening terms form a geometric progression where the common ratio is ⅓:

3/4, 1/4, 1/12, 1/36, 1/108, ...