How many terms of the arithmetic sequence 88, 85, 82, . . . appear before the number \(-171 \) appears?
+130070 Actually , -171 will not appear
The difference between successive terms = -3
So....the nth term is given by
88 - 3 (n -1) =
91 - 3n
But note that no interger n can produce -171 because
-171 = 91 - 3n
-171 - 91 = -3n
-262 = -3n
-262 / -3 = n = 87 1/3 which is not an integer
Your " - 171" should read - 71
Your sequence looks like this:
88 , 85 , 82 , 79 , 76 , 73 , 70 , 67 , 64 , 61 , 58 , 55 , 52 , 49 , 46 , 43 , 40 , 37 , 34 , 31 , 28 , 25 , 22 , 19 , 16 , 13 , 10 , 7 , 4 , 1 , -2 , -5 , -8 , -11 , -14 , -17 , -20 , -23 , -26 , -29 , -32 , -35 , -38 , -41 , -44 , -47 , -50 , -53 , -56 , -59 , -62 , -65 , -68 , -71 , -74 , >>Number of terms = 55>>Total Sum == 385
So, -71 would be the 54th term.
