How many terms of the arithmetic sequence 88, 85, 82, . . . appear before the number -17 appears?

Guest Jul 20, 2017

#1**+1 **

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.

Guest Jul 20, 2017

edited by
Guest
Jul 20, 2017

#2**+1 **

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

CPhill Jul 21, 2017