数列{an}是等差数列,数列{bn}满足条件bn=0.5的an次方,已知b1+b2+b3=21/8,上接 b1b2b3=1/8,求数列{an}的通项公式

数列{an}是等差数列,数列{bn}满足条件bn=0.5的an次方,已知b1+b2+b3=21/8,上接 b1b2b3=1/8,求数列{an}的通项公式
数列{an}是等差数列,数列{bn}满足条件bn=0.5的an次方,已知b1+b2+b3=21/8,
上接 b1b2b3=1/8,求数列{an}的通项公式

数列{an}是等差数列,数列{bn}满足条件bn=0.5的an次方,已知b1+b2+b3=21/8,上接 b1b2b3=1/8,求数列{an}的通项公式
a(n) = a + (n-1)d.
b(n) = (1/2)^[a(n)] = (1/2)^[a+(n-1)d].
21/8 = b(1) + b(2)+b(3) = (1/2)^(a) + (1/2)^(a+d) + (1/2)^(a+2d),
1/8 = b(1)b(2)b(3) = (1/2)^[a+a+d+a+2d] = (1/2)^[3a+3d] = (1/8)^(a+d),
1 = a+d,
a = 1 - d,
a+2d = 1+d.
21/8 = (1/2)^(a) + (1/2)^(a+d) + (1/2)^(a+2d) = (1/2)^(1-d) + (1/2) + (1/2)^(1+d),
21/4 = (1/2)^(-d) + 1 + (1/2)^(d),
17/4 = (1/2)^(-d) + (1/2)^d,
(17/4)*(1/2)^(d) = 1 + (1/2)^(2d),
记x = (1/2)^(d),
则,0 = x^2 - 17x/4 + 1,
Delta = (17/4)^2 - 4 = [289 - 64]/16 = 225/16 = (15/4)^2,
x = [17/4 + 15/4]/2 = 4
或x = [17/4 - 15/4]/2 = 1/8.
4 = (1/2)^d,d = -2
或 1/8 = (1/2)^d,d=3.
a = 1-d = 1-(-2) = 3或
a = 1-d = 1-3 = -2
a(n) = 3 -2(n-1) = 5-2n
或a(n) = - 2 + 3(n-1) = 3n-5

童鞋，想问一下，“bn=0.5的an次方”的意思是bn=（0.5）^(an)。对么？