Question

记公差d≠0的等差数列{an}的前n项和为Sn,一直a1=2+根号2,S3=12+3根号2.记bn=an-根号2,若自然

Answer 1

a(n)=a+(n-1)d=2+2^(1/2) + (n-1)d.

s(n) = na + n(n-1)d/2 = n[2+2^(1/2)] + n(n-1)d/2,

12 + 3(2)^(1/2) = s(3) = 3[2+2^(1/2)] + 3d,d = 2.

a(n) = 2+2^(1/2) + 2(n-1).

b(n) = a(n) - 2^(1/2) = 2+2(n-1)=2n.

b[n(k)] = 2n(k) = b[n(1)]*q^(k-1) = 2n(1)*q^(k-1) = 2q^(k-1),

b[n(2)] = 2n(2) = 6 = 2q,q = 3.

b[n(k)] = 2n(k) = 2q^(k-1) = 2*3^(k-1),

n(k) = 3^(k-1)