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Question

A carpenter was hired to build $$192$$ window frames. The first day he made $$5$$ frames and each day, thereafter he made $$2$$ more frames than he made the day before. How many days did he take to finish the job?


Solution

We have $$5+7+9+.....=192$$

As we know, $$S_n=\dfrac n2 \{2a+(n-1)d\}..............where \ a=first \  term, \ n=no. \ of \ terms, \ d=common \ difference$$

$$\Rightarrow \dfrac{n}{2}\times [10+(n-1)\times 2]=192$$

$$\Rightarrow n(n+4)=192$$

$$\Rightarrow n^2+4n-192=0$$

$$\Rightarrow (n+16)(n-12)=0$$

$$\Rightarrow n=12 ......as \ n \  can't \  be \  equal \  to \ -16$$.

Mathematics

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