To find the general formula for an arithmetic sequence, we can use the formula for the \(n\)-th term of an arithmetic sequence, which is:
\[ a_n = a_1 + (n - 1) d \]
where \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.
From the terms provided in the problem, we have:
- \(a_2 = 17\)
- \(a_3 = 29\)
- \(a_4 = 41\)
- \(a_7 = 77\)
From \(a_2\) to \(a_3\), we can calculate the common difference \(d\):
\[ d = a_3 - a_2 = 29 - 17 = 12 \]
Similarly, we can check the difference from \(a_3\) to \(a_4\):
\[ d = a_4 - a_3 = 41 - 29 = 12 \]
The common difference \(d = 12\) is consistent.
Next, we can find \(a_1\). Using the equation for \(a_2\):
\[ a_2 = a_1 + (2 - 1) d \] \[ 17 = a_1 + 12 \] \[ a_1 = 17 - 12 = 5 \]
Now we have \(a_1 = 5\) and \(d = 12\). We can write the general term of the arithmetic sequence:
\[ a_n = a_1 + (n - 1) d = 5 + (n - 1) \cdot 12 \] \[ a_n = 5 + 12(n - 1) = 5 + 12n - 12 = 12n - 7 \]
So, the formula representing the term of the sequence is:
\[ a_n = 12n - 7 \]
Next, we can find the 75th term, \(a_{75}\):
\[ a_{75} = 12 \cdot 75 - 7 \] \[ = 900 - 7 \] \[ = 893 \]
Thus, the 75th term is:
\[ \boxed{893} \]
The answer is C. 893.