To find the missing numbers in the sequence, let's first look at the differences between the known numbers:
- From \( 34 \) to \( 26 \): \( 34 - 26 = 8 \)
- From \( 26 \) to the next number (let's call it \( x \)):
- From \( x \) to \( 10 \):
- From \( 10 \) to \( 2 \): \( 10 - 2 = 8 \)
- From \( 2 \) to \( -6 \): \( 2 - (-6) = 8 \)
It seems that the sequence is decreasing by \( 8 \) each time. If we apply the same logic in reverse:
- Starting from \( 34 \) and adding \( 8 \) gives us \( 34 + 8 = 42 \). So, the first missing number is \( 42 \).
- From \( 26 \), we need to find the previous number before it. If it's decreasing by \( 8 \), then the number before \( 26 \) is \( 26 + 8 = 34 \).
Thus, the entire sequence filled in is:
42, 34, 26, 18, 10, 2, -6.
So, the missing numbers are \( 42 \) and \( 18 \).