Final answer:
The nth term of the sequence 9, 17, 25, 33, 41 is found using the formula an = 8n + 1, where n represents the term's position in the sequence.
Step-by-step explanation:
The student is asking for the nth term of the sequence 9, 17, 25, 33, 41. To find the nth term of this arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and d is the common difference between the terms.
The first term a1 is 9, and the common difference d is found by subtracting the first term from the second term, giving us 17 - 9 = 8. Thus, the formula for the nth term is an = 9 + (n - 1) × 8, which simplifies to an = 8n + 1.
Therefore, to find any term in the sequence, simply plug the value of n into this formula.
To determine the nth term of the sequence 9, 17, 25, 33, 41, we can observe that each term is obtained by adding 8 to the previous term. This means that the sequence follows an arithmetic progression with a common difference of 8.
The formula for finding the nth term of an arithmetic progression is:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
In our case, a1 = 9 and d = 8. Plugging in these values, we can find the nth term. For example, to find the 6th term:
a6 = 9 + (6-1)(8) = 9 + 5(8) = 9 + 40 = 49
Therefore, the nth term of the sequence 9, 17, 25, 33, 41 is given by an = 9 + (n-1)(8)