Question Number 160894 by HongKing last updated on 08/Dec/21
Answered by Kamel last updated on 09/Dec/21
$${a}_{{n}+\mathrm{1}} ={a}_{{n}+\mathrm{2}} −{a}_{{n}+\mathrm{3}} +{a}_{{n}} −{a}_{{n}+\mathrm{1}} \\ $$$${a}_{\mathrm{1}} +\underset{{k}=\mathrm{1}} {\overset{\mathrm{2021}} {\sum}}{a}_{{n}+\mathrm{1}} ={a}_{\mathrm{3}} −{a}_{\mathrm{2024}} +\mathrm{2}{a}_{\mathrm{1}} −{a}_{\mathrm{2022}} =\mathrm{2}+\mathrm{2}+\mathrm{4}−\mathrm{3}=\mathrm{5} \\ $$$${a}_{\mathrm{2024}} ={a}_{\mathrm{2023}} −\mathrm{2}{a}_{\mathrm{2022}} +{a}_{\mathrm{2021}} =−{a}_{\mathrm{2021}} −{a}_{\mathrm{2022}} +{a}_{\mathrm{2020}} \\ $$
Commented by HongKing last updated on 10/Dec/21
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{mych}\:\mathrm{dear}\:\mathrm{Sir} \\ $$