If-12-x-y-and-4-provides-a-sequence-such-that-the-first-3-of-the-numbers-are-in-arithmetic-progression-Calculate-the-a-Possible-values-of-x-and-y-b-The-sum-of-the-A-P-c-The-product-of-the-la

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Question Number 10318 by Tawakalitu ayo mi last updated on 03/Feb/17

$$\mathrm{If}12,\mathrm{x},\mathrm{y}\mathrm{and}4\mathrm{provides}\mathrm{a}\mathrm{sequence}\mathrm{such}\mathrm{that}$$$$\mathrm{the}\mathrm{first}3\mathrm{of}\mathrm{the}\mathrm{numbers}\mathrm{are}\mathrm{in}\mathrm{arithmetic}$$$$\mathrm{progression}.\mathrm{Calculate}\mathrm{the}$$$$\left(\mathrm{a}\right)\mathrm{Possible}\mathrm{values}\mathrm{of}\mathrm{x}\mathrm{and}\mathrm{y}$$$$\left(\mathrm{b}\right)\mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{A}.\mathrm{P}$$$$\left(\mathrm{c}\right)\mathrm{The}\mathrm{product}\mathrm{of}\mathrm{the}\mathrm{last}3\mathrm{numbers}\mathrm{of}$$$$\mathrm{the}\mathrm{G}.\mathrm{P}$$

Answered by mrW1 last updated on 05/Feb/17

$$\left(a\right)$$$$thefirst3numbersareinA.P.$$$$\Rightarrow y-x=x-12\left(i\right)$$$$thelast3numbersareinG.P.:$$$$\Rightarrow \frac{4}{y}=\frac{y}{x}\left(ii\right)$$$$$$$$from\left(i\right)weget:$$$$y=2x-12=2(x-6)$$$$$$$$from\left(ii\right)weget:$$$$y^2=4x$$$$4(x^2-12x+36)=4x$$$$x^2-13x+36=0$$$$x=\frac{13\pm \sqrt{{13}^2-4\times 36}}{2}=\frac{13\pm 5}{2}=\{\begin{array}{l}9\\ 4\end{array}$$$$y=2(x-6)=\{\begin{array}{l}6\\ -4\end{array}$$$$$$$$thesequenceis$$$$12,9,6,4or$$$$12,4,-4,4$$$$$$$$\left(b\right)$$$$12+9+6=27or$$$$12+4-4=12$$$$$$$$\left(c\right)$$$$9\times 6\times 4=216or$$$$4\times (-4)\times 4=-64$$

Commented by Tawakalitu ayo mi last updated on 04/Feb/17

$$\mathrm{I}\mathrm{really}\mathrm{appreciate}\mathrm{your}\mathrm{effort}\mathrm{sir}.\mathrm{God}\mathrm{bless}$$$$\mathrm{you}\mathrm{sir}.$$

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