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Insert three fractions between 1/4 and 1/3 so the five fractions form an arithmetic sequence. What is the sum, expressed as a common fraction, of these three new fractions?

 Jun 22, 2021
 #1
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1/4 = first term           1/3  = 5th term

 

So.....

 

1/4  +  4d   =    1/3

 

4d  =  1/3  - 1/4

 

4d  = 1/12

 

d  =1/48

 

1/4 + 1/48 =  13/48  =   2nd term

 

13/48  + 1/48   =  14/48  =  3rd term

 

14/48 +  1/48  =  15/48  =  4th term

 

Sum  =      (13 + 14 + 15)   / 48  =     42  / 48  =    7/8

 

 

cool cool cool

 Jun 22, 2021

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