“微信扫一扫”进入题库练习及模拟考试
若数列 \(\left\{ {{a_n}} \right\}\) 满足 \({a_n} + {a_{n + 1}} + {a_{n + 2}} = 2020\)(\(n \in {{\mathbf{N}}^*}\)) , \({a_{2022}} = 1\),\({a_{2021}} = 2\) ,则 \({a_1} = \) ( )
A.1
B.2
C.3
D.2017
参考答案:D
解析:
因为 \({a_n} + {a_{n + 1}} + {a_{n + 2}} = 2020\) ,
所以 \({a_{n + 1}} + {a_{n + 2}} + {a_{n + 3}} = 2020\) ,
两式相减可得, \({a_n} = {a_{n + 3}}\) ,
所以数列\(\left\{ {{a_n}} \right\}\)为以\(3\)为周期的周期数列,
又因为 \({a_{2020}} + {a_{2021}} + {a_{2022}} = 2020\) ,
即 \({a_{2020}} + 2 + 1 = 2020\) ,所以 \({a_{2020}} = 2017\) ,
因为 \(2020 = 673 \times 3 + 1\) ,所以 \({a_{2020}} = {a_1} = 2017\) .
故选:D