Question

( x +5 ) + ( x + 10 ) + ( x + 15 ) + .... + ( x + 2000 ) = 401800

Answer 1

\(\left(x+5\right)+\left(x+10\right)+\left(x+15\right)+...+\left(x+2000\right)=401800\)

\(\left(x+x+x+...+x\right)+\left(5+10+15+...+2000\right)=401800\)

\(400x+\dfrac{\left(5+2000\right).\left[\left(2000-5\right):5+1\right]}{2}=401800\)

\(400x+\dfrac{2005.400}{2}=401800\)

\(400x+401000=401800\)

\(400x=401800-401000\)

\(400x=800\)

\(x=\dfrac{800}{400}=2\)