Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 601: 32

$a_{n}=-3n+10$ Or: $a_{n}=7-3(n-1)$

We are given: $7, 4, 1, -2$, ... We see that the terms in the sequence go down by $3$ each time. In order to make the first term $7$, we add $10$: $a_1=-3(1)+10$ $a_2=-3(2)+10$ $a_3=-3(3)+10$ $a_4=-3(4)+10$ ... $a_{n}=-3n+10$ Or: $a_{n}=7-3(n-1)$