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Question Number 125851 by harckinwunmy last updated on 14/Dec/20

$$\mathrm{calculate}\mathrm{the}\mathrm{product}\mathrm{of}\mathrm{the}1\mathrm{st}\mathrm{and}4\mathrm{th}\mathrm{terms}$$$$\mathrm{of}\mathrm{the}\mathrm{sequence}\mathrm{whose}\mathrm{mth}\mathrm{term}\mathrm{is}\mathrm{defined}\mathrm{as}$$$${\psi }_{\mathrm{m}+1}=\left(3^{\mathrm{m}}\right){(-2)}^{\mathrm{m}-1}$$

Answered by floor(10²Eta[1]) last updated on 14/Dec/20

$$\mathrm{m}=0\Rightarrow {\psi }_1=3^0{(-2)}^{-1}=\frac{-1}{2}$$$$\mathrm{m}=3\Rightarrow {\psi }_4=3^3{(-2)}^2=108$$$${\psi }_1.{\psi }_4=\left(\frac{-1}{2}\right)\left(108\right)=-54$$

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