Sure, let's tackle this step by step.
An arithmetic sequence is characterized by a common difference, which is the same for each consecutive term of the sequence. The general form for an arithmetic sequence is given by an = a1 + (n-1)d, where a1 represents the first term, n is the position of the nth term, and d is the common difference.
In the given sequence (an = -11 + 7n), a1 can be found by substitifying n = 1 into the formula. So, a1 equals -11 + 7*1 = -4. This is the first term in our sequence.
The common difference for our sequence, denoted by d, can be directly read from the equation. We note that for every one-step increase in n, the term increases by 7, hence the common difference, d, is 7.
From knowing the first term (a1) and the common difference (d), we can find the subsequent terms in the sequence using the general formula (an = a1 + (n-1)d). Given that for the first term n = 1, for the second term n = 2, for the third term n = 3, and so forth.
So the second term of the sequence is a2 = a1 + (2-1)*7 = -4 + 1*7 = 3.
The third term of the sequence is a3 = a1 + (3-1)*7 = -4 + 2*7 = 10.
The fourth term of the sequence is a4 = a1 + (4-1)*7 = -4 + 3*7 = 17.
The fifth term of the sequence is a5 = a1 + (5-1)*7 = -4 + 4*7 = 24.
Therefore, the first five terms of the sequence are -4, 3, 10, 17, 24.
Now, to find the 34th term (a34) of the sequence, we use the same general arithmetic sequence formula (an = a1 + (n-1)d) where n = 34. On substitution, we get a34 = -4 + (34-1)*7 = -4 + 33*7 = 227.
Therefore, the 34th term of the sequence is 227.