Final answer:
The nth term of an arithmetic sequence with first term 13 and second term 213 is found using the common difference, which is 200. Using the formula an = a1 + (n - 1)d, the nth term is an = 200n - 187.
Step-by-step explanation:
To determine the nth term of an arithmetic sequence with the first term 13 and the second term 213, we first need to find the common difference (d). The common difference is the difference between any two consecutive terms, so for this sequence, d = 213 - 13 = 200. Once we have the common difference, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and n is the term number. Therefore, the nth term of this sequence is given by:
an = 13 + (n - 1) × 200
an = 13 + 200n - 200
an = 200n - 187.
Thus, to find the value of any particular term in the sequence, just substitute the term number for n in the equation an = 200n - 187.
In this case, the first term a1 is 13 and the second term a2 is 213. The common difference can be found by subtracting the first term from the second term: 213 - 13 = 200.
Now, we can substitute the values into the formula to find the nth term:
an = 13 + (n - 1)(200)
This is the expression for the nth term of the arithmetic sequence.