+0  
 
+1
99
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100 more than the sum of n consecutive integers is equal to the sum of the next n consecutive integers.  Find n.

 Dec 6, 2019
 #1
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Since you're adding each number, nnext=99:

 

nx=nx-1+x | This is our basic formula

 

nx=nx-1+100 | We know that we're adding 100 to the current x, and the current x is equal to nx-1+x, so the next x must be 100

 

n100=n100-1+100

 

n100=n99+100 | We subtract 1, giving us the previous x

 Dec 6, 2019
 #2
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First sequence begins with:0 to 9 =45 + 100 =145
n =9 - 0 + 1 =10 terms
Second sequence begins with:10 to 19          =145
n =19 - 10 + 1 =10 terms

 Dec 6, 2019

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