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The largest and smallest of three consecutive terms in an arithmetic sequence differ by 14. Half of the smallest term is added to each term and the sum of the resulting three numbers is 120. What is the value of the original smallest term?

Guest Jun 26, 2018
 #1
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Let the smallest term  = a

Let the  next term  = a + d

Let  the largest term  be  a + 2d

 

And we know that     

 (a + 2d)  -  a  = 14

2d  =  14

d  = 7

 

So  we have that

 

a  + a/2  +  (a + 7) + a/2  + (a + 14) + a/2  = 120  simplify

3a +  3a/2  + 21 =  120     

4.5a  + 21  = 120      subtract  21  from both sides

4.5 a  = 99    divide both sides by 4.5

a  = 22 

 

So...the smallest term is 22

 

 

cool cool cool  

CPhill  Jun 27, 2018

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