A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

Explanation

Here , a-=5 and d=2
Let he finshed the job in n days .
then , `S_(n)=192`
`s_(n)=(n)/(2)[2a+(n-1)d]`
`implies 192 =(n)/(2)[2xx5+(n-1)2]`
`implies 192 =(n)/(2)[10+2n-2]`
` implies 192 =(n)/(2) [8+2n]`
`implies 192=4n+n^(2)`
`implies n^(2)+4n-192=0`
`implies (n-12)(n+16)=0`
`implies n=12-16`
`therefore n=12`