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Two arithmetic sequences have the same common difference.  The difference between their 100th terms is 100.  What is the difference between their 1000th terms?

 Feb 20, 2021
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If  they  have  the  same common difference   and  the  difference  of  their 100th terms is  100, then the first term difference  is  also 100

 

So.......the difference  between  their 1000th terms will also be  = 100

 

To  see this, let  the  first term of one series  = n     and the first term of the second series  =  n + 100

 

The  difference  of  the  series  after  ANY  term  = 

 

(n + 100)  +  d ( n  -1)  =     n + 100  +  nd  -  d           (1)

    n    +  d ( n -1)      =        n             + nd   -  d           (2)

 

Subtract  (2)  from (1)

 

100    =   the difference

 

 

cool cool cool

 Feb 20, 2021

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