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Which term of the sequence 20, 19 1/4, 18 1/2, 17 3/4, ..., is the first negative term?

 Feb 18, 2021
 #1
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The  common difference is   -3/4

 

We  can  solve  this  for  n

 

20  -  (3/4)(n - 1)  <  0

 

20  - (3/4) n + 3/4   <   0        multiply  through by  4

 

80  - 3n + 3   <   0

 

83  - 3n <  0

 

83  < 3n      divide  both sides  by 3

 

83/3 < n

 

n > 83/3

 

n > ( 27  + 2/3 )

 

The 28th term  will  be  the first negative one

 

 

cool  cool  cool

 Feb 18, 2021

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