Final answer:
To find the 10th and 101st terms of an arithmetic sequence with a common difference of -16, we use the formula a_n = a_1 + (n - 1)d. The 10th term is -70 and the 101st term is -1526.
Step-by-step explanation:
The student's question involves finding the 10th term and the 101st term of a given sequence. The provided sequence is 74, 58, 42, which is an arithmetic sequence (a sequence where each term after the first is derived by adding a constant number, called the common difference, to the previous term).
To find the common difference, subtract the second term from the first term: 58 - 74 = -16. Thus, the common difference is -16.
To find the nth term of an arithmetic sequence, the formula is:
an = a1 + (n - 1)d,
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
10th Term
Using the formula:
a10 = 74 + (10 - 1)(-16) = 74 - 144 = -70
101st Term
Similarly, for the 101st term:
a101 = 74 + (101 - 1)(-16) = 74 - 1600 = -1526