How many terms of the arithmetic sequence 88, 85, 82, . . . appear before the number -17 appears?
F + (N - 1)*D =Nth term.
88 + (N - 1)*-3=-17
88 -3N + 3 =-17
91 -3N = -17
-3N =-17-91
-3N = -108
N =-108 / -3
N = 36th term number with a value of -17. So, there are 35 terms before -17 appears.
Another way to determine this is to note that the difference between terms is 3
So.....to find out which term is -17, we have....
[ first term - given term ] / difference between terms + 1
[ 88 - (- 17) ] / 3 + 1 =
[ 105 ] / 3 + 1 =
35 + 1
36
So, -17 is the 36th term and 35 terms appear before it