Problem 2

Explanation

The sequence above consists of two alternating sub-sequences (skipping one number).

Pattern 1 (Odd positions)

$42, 39, 34, 27, ...$

The differences between consecutive terms are:

The pattern is subtracting consecutive odd numbers ($-3, -5, -7$). Thus, the next difference is $-9$. Next term: $27 - 9 = 18$.

Pattern 2 (Even positions)

$40, 36, 30, 22, ...$

The differences between consecutive terms are:

The pattern is subtracting consecutive even numbers ($-4, -6, -8$). Thus, the next difference is $-10$. Next term: $22 - 10 = 12$.

So, the next two numbers are $18$ and $12$.