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Question Number 53515 by 0955083339 last updated on 22/Jan/19

$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{ten}\mathrm{odd}\mathrm{numbers}$$$$\mathrm{and}\mathrm{eleven}\mathrm{even}\mathrm{numbers}?$$

Answered by tanmay.chaudhury50@gmail.com last updated on 23/Jan/19

$$S_{odd}=1+3+5+...+[1+(10-1)2]$$$$S_{odd}=1+3+5+...+19$$$$S_{odd}=19+17+15+...+1$$$$add$$$$2S_{odd}=20+20+20...tentimes$$$$2S_{odd}=20\times 10$$$$S_{odd}=100$$$$ordirectformula$$$$S=\frac{n}{2}[2a+(n-1)d]$$$$=\frac{10}{2}[2\times 1+(10-1)2]$$$$=100$$$$S_{even}=2+4+6+...+[2+(11-1)2]$$$$S_{even}=2+4+6+...+22$$$$S_{even}=22+20+18+...+2$$$$add$$$$2S_{even}=24+24+24...eleventimes$$$$2S_{even}=24\times 11$$$$S_{even}=\frac{24\times 11}{2}=132$$$$ordirectformula$$$$S_{even}=\frac{11}{2}[2\times 2+(11-1)2]$$$$S_{even}=\frac{11}{2}\left[24\right]=132$$

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