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Find Formula (Posted on 2012-02-17) Difficulty: 3 of 5
Derive a formula for the product of the first n members of an arithmetic progression with an initial element a and a common difference d;(a*d>0).
Verify the validity of your expression for (a,d,n)=(2,3,8).

See The Solution Submitted by Ady TZIDON    
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Find Formula Solution | Comment 2 of 4 |

 

    Definition :

  (1...q)[F(k) ]  = multiplications of F(k) from k=1 to k=q .

  

      F(k)=(a^2+a*n*d-a*d-n*d^2)+[(n+1)*d^2*k-d^2*k^2] 

    for even n the solution is :

   (1...n/2)[F(k)]

      for odd n, the solution is :

   (a+0.5*d*(n-1) )* (1...(n-1)/2 )F(k)

  

  

  

 

 

   


  Posted by Dan Rosen on 2012-02-19 09:29:55
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