Final answer:
To find the term number n in the arithmetic sequence where the first term is 1, the difference is 8, and the general term is 73, the formula a_n = a_1 + (n - 1)d is used. After substituting the known values and solving for n, we find that n equals 10.
Step-by-step explanation:
To find the number of terms n in an arithmetic progression where the first term is 1, the common difference is 8, and the general term is 73, we use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term, d is the common difference, and n is the number of terms. Substituting the given values:
73 = 1 + (n - 1) × 8
Now, solve for n:
73 = 1 + 8n - 8
73 = 8n - 7
73 + 7 = 8n
80 = 8n
n = 80 / 8
n = 10
So, the number of terms n is 10.