Final answer:
The four hundredth term of the arithmetic sequence starting with 17 and having a common difference of 6 is 2411. To derive this, the formula for the nth term of an arithmetic sequence is applied.
Step-by-step explanation:
The student is asking for help in determining the four hundredth term of a sequence, as well as finding the total number of terms in that sequence. To obtain the four hundredth term of the sequence starting with 17, 23, 29, 35... we can see that this is an arithmetic sequence with the common difference of 6, because each term is obtained by adding 6 to the previous term.
To find the nth term of an arithmetic sequence, we use the formula a_n = a_1 + (n - 1)d where a_1 is the first term, d is the common difference, and n is the term number. For the 400th term, a_400 = 17 + (400 - 1) × 6 = 17 + 399 × 6 = 17 + 2394 = 2411. Therefore, the 400th term is 2411.
In terms of the number of terms in the sequence, the question is not clear if it refers to a finite sequence with an end point or if it's asking how many terms in the sequence exist up to this point. If the latter, then 400 terms exist up to and including the 400th term.