How many terms are in the finite arithmetic sequence 8, 1, -6, ..., -41?

1. Find the common difference: 1 - 8 = -7. 2. Substitute into a_n = a_1 + d(n - 1) to get a_n = 8 + (-7)(n - 1). 3. Expanding gives a_n = 8 - 7n + 7, which simplifies to a_n = 15 - 7n. 4. Set the last term equal to this: -41 = 15 - 7n. 5. Subtracting 15 gives -56 = -7n, so n = 8. 6. There are eight terms in the sequence. 7. Counting how many steps of -7 fit between 8 and -41 gives 7, which is one fewer than the number of terms, and that off-by-one is the trap. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.2 Arithmetic Sequences_