Final answer:
The 22nd term of the arithmetic sequence with a first term of 8 and a ninth term of 56 is calculated to be 134, which is option A.
Step-by-step explanation:
To find the 22nd term of an arithmetic sequence, we first need to determine the common difference (d) using the information provided: a1 = 8 and a9 = 56. The common difference is calculated by subtracting the first term from the ninth term and then dividing by the number of terms between them, which is eight:
d = (a9 - a1) / (9 - 1) = (56 - 8) / 8 = 48 / 8 = 6
Now that we have the common difference, we can find the 22nd term using the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1) × d. For the 22nd term:
a22 = 8 + (22 - 1) × 6 = 8 + 21 × 6 = 8 + 126 = 134
Therefore, the 22nd term of the arithmetic sequence is 134, which corresponds to option A.