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Please explain clearly!

 

 

Part (a): Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1)
in terms of a and n.

Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and 

 

a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100

 Mar 10, 2018
 #1
avatar+103120 
+2

Part (a): Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1)
in terms of a and n.

 

We can write  the above sum as

 

n*a  +  ( 1 + 2 + 3 + ....+ n - 1 )  =

 

n*a   +   (n - 1) (n)/2  =

 

n [ a +  ( n - 1) / 2 ]   =

 

n [ 2a + n - 1] / 2  =

 

(n/2)  [ 2a + n - 1 ]

 

 

cool cool cool

 Mar 10, 2018
 #2
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0

b)

 

a=9    and   n=8

a =18 and   n=5

 Mar 10, 2018

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