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An arithmetic sequence consists of 2197 consecutive positive terms, which sum up to 65^4 and whose first term is a 4-digit prime number. What are the first and the last terms of this sequence? Thank you for help.

 Apr 18, 2020
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A formula to find the sum of an arithmetic sequence is:  Sum  =  N(F + L)/2

   N = number of numbers = 2197

   F = first number

   L = last number = F + 2196

   Sum = 654 = 17,850,625

--->     17,850,625  =  2197( F + (F + 2196) ) / 2

           35,701,250  =  2197( 2F + 2196)

                   16250  =  2F + 2196

                   14054  =  F

                     7027  =  F

 

You can find the last term ...

 Apr 18, 2020

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