How many terms of the arithmetic sequence 88, 85, 82, . . . appear before the number \(-171\) appears?
Nth term ==F + D * (N - 1)
-171 ==88 + - 3 * (N - 1)
- 171 ==88 -3N + 3
-171 ==91 - 3N
-171 - 91 == - 3N
- 262 == - 3N
N ==262 / 3
N==87 1/3 (it should give a whole integer and no fraction, which means there is NO TERM - 171).
Here is your sequence:
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 , -77 , -80 , -83 , -86 , -89 , -92 , -95 , -98 , -101 , -104 , -107 , -110 , -113 , -116 , -119 , -122 , -125 , -128 , -131 , -134 , -137 , -140 , -143 , -146 , -149 , -152 , -155 , -158 , -161 , -164 , -167 , -170 , >>Number of terms = 87>>Total Sum == -3567
The 87th term is - 170 and NOT - 171
+36916 d = -3 for this sequence
88 + (n-1) d = -171
-3n + 3 = - 259 n = 87.33rd term
( this is APPROXIMATELY where -171 would appear.....but there is no 'partial' term, so -171 'exactly' ....won't be in the list )
