SOLUTION: The sum of the first n terms of the Arithmetic Progression 13, 16.5 , 20 is the same as the sum of the first n terms of the Arithmetic progression 3 , 7 , 11 .calculate n.

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Question 823499: The sum of the first n terms of the Arithmetic Progression 13, 16.5 , 20 is the same as the sum of the first n terms of the Arithmetic progression 3 , 7 , 11 .calculate n.
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

The sum of the first n terms of the Arithmetic Progression  13, 16.5 , 20  

is the same as the sum of the first n terms of the Arithmetic progression 3, 7, 11   

calculate n.

S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%29d%29

%28n%2F2%29%2826+%2B+%28n-1%293.5%29+=%28n%2F2%29%283+%2B+%28n-1%294%29++%29 |Multiplying thru by 2/n

26+%2B+%28n-1%293.5+=+3+%2B+%28n-1%294++

       26 + 3.5n - 3.5 = 3 + 4n - 4

         26  - 3.5 +1= .5n

                 23.5 = .5n 

                     n = 47  

   CHECKING our answer***

 26+%2B+%28n-1%293.5+=+3+%2B+%28n-1%294++%29

 +26+%2B+%2846%293.5+=+3+%2B+%2846%294++

      +187+=+187%29