To find the 22nd term of the arithmetic sequence, we first need to identify the first term and the common difference. We know that the first term (a1) is 8, and the ninth term (a9) is 56.
The formula for the n-th term of an arithmetic sequence is:
a_n = a1 + (n – 1) * d
Here, a1 is the first term, d is the common difference, and n is the term number.
We can use the information we have to find d. Since we know:
a9 = a1 + 8d
Substituting the known values:
56 = 8 + 8d
Now, we solve for d:
56 – 8 = 8d
48 = 8d
d = 6
Now that we have the common difference (d = 6), we can find the 22nd term (a22) using the term formula:
a22 = a1 + (22 – 1) * d
a22 = 8 + 21 * 6
a22 = 8 + 126
a22 = 134
Therefore, the 22nd term of the arithmetic sequence is 134.