Question

已知a,x,b和b,y,c成等差数列,而a,b,c成等比数列,求a/x+c/y的值为

等比数列{an}满足下列三个条件:
a1+a2=11,a3*a4=32/9,三个数2/3a2,a3平方,a4+4/9成等差数列,试求数列的通项公式

Answer 1

1)2x=a+b.2y=b+c
b^2=ac
a/x+c/y=2a/(a+b)+2c/(b+c)
=2[a(b+c)+c(a+b)]/(ab+b^2+ac+bc)=2[ab+2ac+bc]/(ab+2ac+bc)=2
2)设公比为q
a1+a2=11 a1(1+q)=11
a3*a4=32/9 a1q^5=32/9
2a3^2=2a2/3+a4+4/9
2a1^2q^4=2a1q/3+a1q^3+4/9=3a1^2q^6/16+a1q^3+a1q^5/8

Answer 2

a,x,b和b,y,c成等差数列,而a,b,c成等比数列,
a+b=2x, b+c=2y, b^2=ac
a/x+c/y=2a/(a+b)+2c/(b+c)
=[2a(b+c)+2c(a+b)]/[(a+b)(b+c)]
=2(ab+2ac+bc)/(ab+ac+b^2+bc)
=2

2.设公比为q,列方程组，死算