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Question Number 174775 by Best1 last updated on 10/Aug/22

Answered by Ar Brandon last updated on 10/Aug/22

p+q=8 ...(i)  p(3^2 )+q+2(2)=52 ⇒9p+q=48 ...(ii)  (ii)−(i)⇒8p=40 ⇒p=5, q=3  ⇒G_n =5×3^(n−1) , A_n =3+2(n−1)=2n+1  A_1 =3: A is true  G_1 =5: B is false  A_3 =7: C is true  G_3 =45: D is true

$${p}+{q}=\mathrm{8}\:...\left({i}\right) \\ $$$${p}\left(\mathrm{3}^{\mathrm{2}} \right)+{q}+\mathrm{2}\left(\mathrm{2}\right)=\mathrm{52}\:\Rightarrow\mathrm{9}{p}+{q}=\mathrm{48}\:...\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right)\Rightarrow\mathrm{8}{p}=\mathrm{40}\:\Rightarrow{p}=\mathrm{5},\:{q}=\mathrm{3} \\ $$$$\Rightarrow{G}_{{n}} =\mathrm{5}×\mathrm{3}^{{n}−\mathrm{1}} ,\:{A}_{{n}} =\mathrm{3}+\mathrm{2}\left({n}−\mathrm{1}\right)=\mathrm{2}{n}+\mathrm{1} \\ $$$${A}_{\mathrm{1}} =\mathrm{3}:\:{A}\:\mathrm{is}\:\mathrm{true} \\ $$$${G}_{\mathrm{1}} =\mathrm{5}:\:{B}\:\mathrm{is}\:\mathrm{false} \\ $$$${A}_{\mathrm{3}} =\mathrm{7}:\:{C}\:\mathrm{is}\:\mathrm{true} \\ $$$${G}_{\mathrm{3}} =\mathrm{45}:\:{D}\:\mathrm{is}\:\mathrm{true} \\ $$

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