In-a-set-of-3-consecutive-natural-numbers-the-sum-of-the-last-2-numbers-is-equal-to-3-times-the-first-numbers-Find-the-sum-of-all-the-three-numbers-

Question Number 95986 by mpym last updated on 29/May/20

$$\mathrm{In}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{3}\:\mathrm{consecutive}\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{2}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{3}\:\mathrm{times}\:\mathrm{the}\:\mathrm{first}\:\mathrm{numbers}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{three}\:\mathrm{numbers}. \\ $$

Commented by mr W last updated on 29/May/20

$${n}−\mathrm{1},\:{n},\:{n}+\mathrm{1} \\ $$$${n}+\left({n}+\mathrm{1}\right)=\mathrm{3}\left({n}−\mathrm{1}\right) \\ $$$$\Rightarrow{n}=\mathrm{4} \\ $$$$\Sigma=\mathrm{3}+\mathrm{4}+\mathrm{5}=\mathrm{12} \\ $$

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