# Solve the equation 73+74+75+...+1236 = 1000x

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The equation could be written :

1+2+3+72+...+73+74+...+1236-(1+2+3+...+72)=1000x

618*1237-36*73=1000x

764466-2628=1000x

761838=1000x

**x=761.838**

Left side of the equation is an arithmetic progression with first term a1=73 and the last term is 1236, the common difference 1 between the successive terms. There are n=1236-73+1 =1164 terms.The sum to n terms are given by,

Sn = (a1+an)n/2

=(73+1236)(1164/2)

=761838.

Therefore the equation to solve now is

1000x=761838.

x=761738/1000 = 761.838.

Hope this helps.