Final answer:
To find the nth term of an arithmetic sequence with the given terms, we use the formula A_n = A_1 + (n - 1)d. By solving the equations formed by substituting the given terms into the formula, we can find the values of A_1 and d. Using these values, we can find the nth term of the sequence.
Step-by-step explanation:
To find the nth term of an arithmetic sequence, we can use the formula:
A_n = A_1 + (n - 1)d
where A_n is the nth term, A_1 is the first term, n is the position of the term, and d is the common difference between consecutive terms.
Given the two terms A6 = 13 and A14 = 25, we can use these values to find the common difference d.
Substituting A6 = 13 and n = 6 into the formula, we get:
13 = A_1 + (6 - 1)d
Substituting A14 = 25 and n = 14 into the formula, we get:
25 = A_1 + (14 - 1)d
Solving these two equations simultaneously will give us the values of A_1 and d.
Once we have the value of d, we can use the formula A_n = A_1 + (n - 1)d to find the nth term of the arithmetic sequence.
Therefore, the correct option is a) A_n = 13 + 12n.