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Question Number 12326 by sin (x) last updated on 19/Apr/17

$$\underset{n=1}{\prod ^x}{a}_n=9^{x!}$$$$a_4=?$$

Answered by nume1114 last updated on 19/Apr/17

$$a_x=\frac{a_1\times a_2\times ...\times a_{x-1}\times a_x}{a_1\times a_2\times ...\times a_{x-1}}$$$$=\frac{\underset{n=1}{\prod ^x}{a}_n}{\underset{n=1}{\prod ^{x-1}}{a}_n}=\frac{9^{x!}}{9^{(x-1)!}}=9^{x!-(x-1)!}$$$$a_4=9^{4!-(4-1)!}=9^{24-6}=9^{18}$$

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