Final answer:
The nth term of the given arithmetic sequence is found using the formula 'an = a1 + (n - 1)d'. In this case, the nth term formula is 'an = 34n - 22' where n is the term number in the sequence.
Step-by-step explanation:
To determine the nth term of the given sequence 12, 46, 80, 114, 148, we first identify the pattern of the sequence. Each term increases by a constant difference, known as the common difference in an arithmetic sequence. In this case, the difference between consecutive terms is 34 (46 - 12 = 34, 80 - 46 = 34, etc.). The nth term in an arithmetic sequence is given by the formula 'an = a1 + (n - 1)d', where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
The first term a1 is 12, and the common difference d is 34. Plugging these into the formula, we get 'an = 12 + (n - 1) × 34'. Simplifying the equation, the nth term formula for this sequence is 'an = 34n - 22'.
The given sequence is 12, 46, 80, 114, 148. To determine its nth term, we need to find the pattern or rule that governs the sequence. By observing the sequence, we can see that each term is obtained by adding 34 to the previous term. Using this information, we can write the expression for the nth term as:
Tn = Tn-1 + 34
where Tn represents the nth term, and Tn-1 represents the (n-1)th term.
Therefore, the nth term of the given sequence is Tn = T1 + 34(n-1), where T1 is the first term, which is 12 in this case.