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

 Jan 20, 2021
 #1
avatar+41 
+2

(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)

So 35 terms appear BEFORE -17.

 Jan 20, 2021
 #2
avatar+116126 
+1

THX, IWTH!!!   .....Here's a little easier way

 

First  term  =  88

Common difference  =   -3

 

We have

 

88  -  3(n -1)  =   -17            where -17   is the  nth term          

 

88 - 3n + 3    = -17

 

-3n  + 91   =  -17

 

-3n =  -108

 

n =  -108/-3   =  36th term

 

So.....35 terms appear  before  -17.....just as IWTH  found  !!!!

 

 

cool cool cool

 Jan 20, 2021

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