Final answer:
To find the equation determining the nth term of the arithmetic sequence, calculate the common difference using the 4th and 10th terms, then solve for the first term, and use them to write the general formula for the nth term.
Step-by-step explanation:
To determine the value of the nth term in an arithmetic sequence given the 4th term and the 10th term, we first need to find the common difference of the sequence. To do so, we can use the fact that in an arithmetic sequence, the difference between consecutive terms is constant. The difference between the 10th term (98) and the 4th term (74) is 98 - 74 = 24, and since there are 10 - 4 = 6 intervals between the 4th and 10th term, the common difference d is 24 / 6, which is 4.
Now that we have the common difference, we can find the first term of the sequence a1 by using the 4th term. The 4th term can be expressed as a1 + 3d (since it is the fourth term, there are three intervals before it). This gives us the equation 74 = a1 + 3(4). Solving for a1 gives us a1 = 62.
Finally, the general formula for the nth term an of the sequence is given by:
an = a1 + (n - 1)d
Substituting our values in, we get:
an = 62 + (n - 1)(4)