Question

Pls help me answer this question and find the value of y. Thx!!

Answer 1

`\large\boxed{y=909}`

Explanation:

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