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Question Number 65901 by byaw last updated on 05/Aug/19

	Answered by MJS last updated on 05/Aug/19

	$a_{0}$ $a_{3} = a_{0} + 2 α$ $a_{8} = a_{0} + 7 α$ $g_{0} = a_{0}$ $g_{1} = γ g_{0} = a_{3}$ $g_{2} = γ g_{1} = a_{8}$ $γ = \frac{a_{3}}{a_{0}} = \frac{a_{8}}{a_{3}}$ $\Rightarrow a_{3}^{2} = a_{0} a_{8}$ ${(a_{0} + 2 α)}^{2} = a_{0} (a_{0} + 7 α)$ $4 a_{0} + 4 α = 7 a_{0}$ $α = \frac{3}{4} a_{0}$ $g_{0} = a_{0}$ $g_{1} = \frac{5}{2} a_{0}$ $g_{2} = \frac{25}{4} a_{0}$ $\Rightarrow γ = \frac{5}{2}$ $g_{0} + g_{1} + g_{2} = \frac{39}{4} a_{0} = 28 \Rightarrow a_{0} = \frac{112}{39} = g_{0}$ $\Rightarrow α = \frac{28}{13}$
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