Final answer:
To determine the nth term of the given sequence 1, 801, 1601, 2401, 3201, you can use the formula nth term = 1 + (n-1) * 800.
Step-by-step explanation:
The given sequence is 1, 801, 1601, 2401, 3201. To determine the nth term, we can observe that each term is obtained by adding a constant difference of 800 to the previous term. So, the formula to find the nth term is:
nth term = 1 + (n-1) * 800
For example, the first term (n=1) is 1, the second term (n=2) is 1 + (2-1) * 800 = 801, the third term (n=3) is 1 + (3-1) * 800 = 1601, and so on.
To determine the nth term of a sequence, we need to find the pattern that the sequence follows. Let's examine the given sequence: 1, 801, 1601, 2401, 3201 First, notice the difference between consecutive terms: 801 - 1 = 800 1601 - 801 = 800 2401 - 1601 = 800 3201 - 2401 = 800
The difference between terms is constant, which means the sequence is an arithmetic sequence. In an arithmetic sequence, each term is equal to the previous term plus a constant difference (d). Given this, the nth term of an arithmetic sequence can be found using 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 term number, d is the common difference.
From the sequence given: a_1 = 1 (the first term), d = 800 (the common difference). Now we can plug these values into the formula to find the nth term: a_n = 1 + (n - 1) * 800 Simplifying the formula gives us: a_n = 1 + 800n - 800 a_n = 800n + 1 - 800 a_n = 800n - 799 So the nth term of the given sequence is 800n - 799