To determine a1, d, and a9 in the given arithmetic sequence, we need to calculate the common difference (d) first.

Using the formula for arithmetic sequences:
an = a1 + (n-1)d

where:
an is the nth term
a1 is the first term
d is the common difference
n is the number of terms

Given that a8 = 126 and a10 = 146:

a8 = a1 + 7d = 126
a10 = a1 + 9d = 146

Subtracting the first equation from the second equation:

a10 - a8 = 2d = 20
d = 10

Now that we know that the common difference is 10, we can find a1 and a9:

a1 = a8 - 7d = 126 - 70 = 56
a9 = a1 + 8d = 56 + 8(10) = 56 + 80 = 136

Therefore, a1 = 56, d = 10, and a9 = 136.