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Question Number 107353 by Yusufa last updated on 10/Aug/20

$$If\mathrm{a}\mathrm{b}13\mathrm{c}\mathrm{d}25\mathrm{are}\mathrm{six}\mathrm{consecutive}\mathrm{terms}\mathrm{of}\mathrm{an}\mathrm{A}P.findtbevalueofabcandd.$$

Answered by john santu last updated on 10/Aug/20

$$\divideontimes \mathrm{JS}\divideontimes$$$$\Rightarrow 13-2\lambda ,13-\lambda ,13,13+\lambda ,13+2\lambda ,13+3\lambda$$$$\mathrm{so}13+3\lambda =25\Rightarrow \lambda =4$$$$\mathrm{now}\mathrm{you}\mathrm{get}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}$$

Answered by nimnim last updated on 10/Aug/20

$$Letxbethecommondifference$$$$\therefore a+2x=13........\left(1\right)$$$$anda+5x=25........\left(2\right)$$$$\left(1\right)-\left(2\right)\to -3x=-12$$$$\Rightarrow x=4$$$$from\left(1\right),a+2\left(4\right)=13$$$$\Rightarrow a=5$$$$AP:5,9,13,17,21,25$$

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