SOLUTION: The sum of the consecutive integers from -17 to x is 100. What is x?

Algebra.Com
Question 984808: The sum of the consecutive integers from -17 to x is 100. What is x?
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The sum of the consecutive integers from −17 to x is 100. What is x?
=============
The sum from -17 to +17 is zero for 35 integers.
---
Now find integers starting at 18 whose sum is 100.
----


(n-5)*(n+40) = 0
n = 5
-------------
40 integers total
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
The sum of the consecutive integers from -17 to x is 100. What is x?

  an = a1 + (n-1)   
     x = -17 + (n-1)1     
     x = -17 + n - 1     
     x = n - 18
x + 18 = n

Sn = [2a1 + (n-1)d]

100 = [2(-17)+(n-1)1]

Multiply both sides by 2


200 = n[-34+(n-1)]

200 = n[-34+n-1]

200 = n(n-35)

Substitute x+18 for n

200 = (x+18)(x+18-35)

200 = (x+18)(x-17)

200 = x²+x-306

0 = x²+x-506

Since the leading coefficient is 1 and 
the middle coefficient is small compared to 506,
the numbers we need have to be near the square 
root of 506, which is about 22.49. So
the factoring numbers are near that:

0 = (x-22)(x+23) 

      x=22, x=-23.

x has to be positive so the answer is 22.


Edwin
RELATED QUESTIONS

If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value (answered by bucky)
If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value (answered by ankor@dixie-net.com)
how do I find the sum of consecutive integers from 17 to 97? what is the formula for it? (answered by richwmiller)
What is the first of 100 consecutive odd integers whose sum is... (answered by ikleyn)
if the sum of the consecutive integers from -22 through x is 72, what is the value of... (answered by checkley77)
The sum of 40 consecutive integers is 100. What is the smallest of these 40... (answered by Boreal)
What is the sum of all integers from -100 to... (answered by arallie)
The sum of four consecutive positive integers is 'X". What is the sum of the second and... (answered by josgarithmetic)
Three times the sum of three consecutive integers x, x + 1, and x + 2, is 72. What are... (answered by mananth)