Answer:
[tex]\large\boxed{y=909}[/tex]
Step-by-step explanation:
[tex]\text{We have}\\\\1+2+3+...+n=\dfrac{n(n+1)}{2}\qquad(*)\\\\3+6+9+...+300=\dfrac{50y}{3}\\-------------\\\\3+6+9+...+300=3(1+2+3+...+100)\qquad(**)\\\\\text{From}\ (*)\ \text{for n = 100 we have}\\\\1+2+3+...+100=\dfrac{100(100+1)}{2}=\dfrac{50(101)}{1}=5050\\\\\text{put it to}\ (**):\\\\3(1+2+3+...+100)=3\cdot5050=15150\\\\\text{Therefore we have the equation:}\\\\\dfrac{50y}{3}=15150\qquad\text{multiply both sides by 3}\\\\50y=45450\qquad\text{divide both sides by 50}\\\\y=909[/tex]
