In-an-arithmetic-progression-the-sum-of-the-third-term-and-8th-term-is-49-and-the-sum-of-the-5th-and-9th-term-is-58-Find-the-first-term-and-the-common-difference-using-simultaneous-equations-

Question Number 101185 by Shazneen last updated on 01/Jul/20

$$Inanarithmeticprogressionthesumofthethirdtermand8thtermis49andthesumofthe5thand9thtermis58.Findthefirsttermandthecommondifferenceusingsimultaneousequations.$$

Answered by $@y@m last updated on 01/Jul/20

$$a+2d+a+7d=49\mathrm{\&}a+4d+a+8d=58$$$$2a+9d=49$$$$2a+12d=58$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$$$3d=9$$$$d=3$$$$2a+9\times 3=49$$$$2a=49-27$$$$2a=22$$$$a=11$$

Commented by smridha last updated on 01/Jul/20

$$\mathit{t}\mathit{h}\mathit{a}\mathit{t}\mathit{s}\mathit{n}\mathit{o}\mathit{t}\mathit{t}\mathit{r}\mathit{u}\mathit{e}..$$$$\mathit{a}\mathit{n}\mathit{s}:$$$$\mathit{a}=11\mathit{a}\mathit{n}\mathit{d}\mathit{d}=3$$

Commented by Rasheed.Sindhi last updated on 01/Jul/20

$$\mathrm{\$}@y@msir{you}^{\prime }vemistakenly$$$$addinsteadtosubtract\dots$$$$Areyouold{}^{\prime }s@ty@m^{\prime }?$$

Commented by $@y@m last updated on 01/Jul/20

������ Hurry makes worry. I had doubt on my solution and I though I will check it later when I am free. No. I am young Satyam. ������ But after updating app, I am not able to login as my recent account Satyam123.

Commented by bemath last updated on 01/Jul/20

$$\mathrm{hahaha}\dots .{\mathrm{i}}^{\prime }\mathrm{m}\mathrm{young}\mathrm{boy}\mathrm{too}$$

Answered by Dwaipayan Shikari last updated on 01/Jul/20

$$supposeaisfirsttermdisthecommondifference$$$$soa+2d+a+7d=49\Rightarrow 2a+9d=49$$$$$$$$a+4d+a+8d=58\Rightarrow 2a+12d=58$$$$3d=9\Rightarrow d=3$$$$a=11$$

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