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Question

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?


Solution

Solution:
Here we have, total no. of frames to be made $$=192$$

The first day he made five frames $$a_1=5$$

Second day $$=a_2=7$$

$$\Rightarrow $$ This will form a ourthematic progeremium with $$a=2$$

Let the carpenter finish the job in $$n$$ days 

Then $$S_{n}=192$$

and $$S_{n}=\dfrac {n}{2}[2a+(n-1)d]=192$$

$$\Rightarrow \ \dfrac {n}{2}[2\times 5+(n-1)2]=192$$

$$\Rightarrow \dfrac {n}{2}[2\times 5+(n-1)2]=192$$

 $$\Rightarrow n=12$$

Mathematics

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