Question 316907
You have an arithmetic progression with a starting value of 200000 and a difference of 1800.
{{{An=200000+1800*(n-1)}}}, with n=1,2,3,...
The sum of an arithmetic progression is given as,
{{{Sn=(1/2)(2A1+d(n-1))n}}}
{{{(1/2)(2(200000)+1800(n-1))n=150000000}}}
{{{400000n+1800n(n-1)=300000000}}}

{{{400000n+1800n^2-1800n=300000000}}}
{{{1800n^2+398200-300000000=0}}}
{{{18n^2+3982n-3000000=0}}}
{{{9n^2+1991n-1500000=0}}}
Using the quadratic equation, 
{{{N=312.6}}}
You will be able to buy the 312th item but won't have enough money left for the next item.