1,5,17,53的规律用n表示.a1=1, a2=5, a3=17,a4=53,an=?给出满意答案会追加悬赏_数学解答

1,5,17,53的规律
用n表示.a1=1, a2=5, a3=17,a4=53,an=?
给出满意答案会追加悬赏

人气：363 ℃　时间：2020-06-27 18:37:24

解答

a2 - a1 = 4 = 4*1;a3 - a2 = 12 = 4*3;a4 - a3 = 36 = 4*9=4*3^2推测an - a(n-1) = 4*3^(n - 2)an = (an - a(n - 1)) + (a(n - 1) + a(n - 2)) +...+(a2 - a1) + 1= 1 + 4(1 + 3 + 3^2 +...+3^(n - 2))= 1 + 4*(3^(...