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Question Number 41381 by behi83417@gmail.com last updated on 06/Aug/18

Commented by tanmay.chaudhury50@gmail.com last updated on 06/Aug/18

$$questionno2)isitAPorGP$$

Commented by behi83417@gmail.com last updated on 06/Aug/18

$$\text{You can't use 'macro parameter character \#' in math mode}$$

Commented by $@ty@m last updated on 06/Aug/18

$$APhasacommondifference$$$$notacommonratio.$$

Commented by behi83417@gmail.com last updated on 06/Aug/18

$$ok.youareright.itisatypo.$$$$\mathit{s}\mathit{u}\mathit{m}\mathit{o}\mathit{f}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{m}\mathit{s}=\mathit{N}$$$$\mathit{s}\mathit{u}\mathit{m}\mathit{o}\mathit{f}\mathit{m}\mathit{t}\mathit{e}\mathit{r}\mathit{m}\mathit{s}=\mathit{M}$$$$\mathit{c}\mathit{o}\mathit{m}\mathit{m}\mathit{o}\mathit{n}\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{c}\mathit{e}=?$$

Answered by tanmay.chaudhury50@gmail.com last updated on 06/Aug/18

$$A+(m-1)D=\frac{1}{n}$$$$A+(n-1)D=\frac{1}{m}$$$$(m-n)D=\frac{1}{n}-\frac{1}{m}$$$$(m-n)D=\frac{m-n}{mn}D=\frac{1}{mn}$$$$A+(m-1)\times \frac{1}{mn}=\frac{1}{n}$$$$A=\frac{1}{n}-\frac{m-1}{mn}=\frac{m-m+1}{mn}=\frac{1}{mn}$$$$so{a}_{mn}=A+(mn-1)\times D$$$$=\frac{1}{mn}+(mn-1)\times \frac{1}{mn}$$$$=\frac{1}{mn}(1+mn-1)=1$$$$$$

Answered by tanmay.chaudhury50@gmail.com last updated on 07/Aug/18

$$2)N=\frac{n}{2}[2a+(n-1)d]]$$$$M=\frac{m}{2}.[2a+(n-1d]$$$$2a+(n-1)d=\frac{2N}{n}$$$$2a+(m-1)d=\frac{2M}{m}$$$$(n-1-m+1)d=\frac{2N}{n}-\frac{2M}{m}$$$$d=\frac{2(\frac{N}{n}-\frac{M}{m})}{n-m}$$

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