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

Guest Jul 20, 2017
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 #1
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+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
avatar+75333 
+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

 

 

cool cool cool

CPhill  Jul 21, 2017

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