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Question Number 175004 by saboorhalimi last updated on 15/Aug/22

Commented by kaivan.ahmadi last updated on 15/Aug/22

$$s_9=6s_6\Rightarrow \frac{9}{2}(2a+8d)=6\times 3(2a+5d)$$$$\Rightarrow 9a+36d=36a+90d$$$$\Rightarrow -27a=54d\Rightarrow \mathrm{d}=\frac{-1}{2}\mathrm{a}$$$$\mathrm{so}$$$$\frac{{\mathrm{a}}_{10}}{{\mathrm{a}}_4}=\frac{\mathrm{a}+9\mathrm{d}}{\mathrm{a}+3\mathrm{d}}=\frac{\mathrm{a}-\frac{9}{2}\mathrm{a}}{\mathrm{a}-\frac{3}{2}\mathrm{a}}=\frac{\frac{-7}{2}\mathrm{a}}{\frac{-1}{2}\mathrm{a}}=7$$

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