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How many terms of the arithmetic sequence 88, 85, 82, . . . appear before the number \(-171 \) appears?

 Apr 6, 2022
 #1
avatar+124594 
+1

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

 

 

cool cool cool

 Apr 6, 2022
 #2
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+1

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.

 Apr 6, 2022

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