Final answer:
To find the 31st term of an arithmetic series, we can use the formulas for the sum of the terms and the position of a term. By solving a system of equations using the given information, we can find the values of the first term and the common difference. Finally, we can use these values to find the 31st term.
Step-by-step explanation:
First, we need to find the common difference of the arithmetic series. Since the 12th term is given as 69, we can use the formula tn = a + (n - 1)d, where tn is the nth term, a is the first term, n is the position of the term, and d is the common difference. Plugging in the values, we get 69 = a + (12 - 1)d. Now, we have another equation from the sum of the 18 terms. The formula for the sum of an arithmetic series is Sn = n/2(a + l), where Sn is the sum of the first n terms, a is the first term, and l is the last term. Plugging in the given values, we have 4426 = 18/2(a + l). Now, we have a system of two equations. Solving them will give us the values of a and d, which we can use to find the 31st term by plugging in the values into the formula tn = a + (n - 1)d.