Question

等比数列中，公比q≠1,a1,a3,a5是等差数列{bn}中的b2,b4,b12,则q=

Answer 1

等比数列：a3=a1*q^2；a5=a1*q^4
等差数列：b4=b2+2d；b12=b2+10d
所以：2d=b4-b2=a3-a1=a1*(q^2-1)
10d=b12-b2=a5-a1=a1*(q^4-1)
两式相除：5=(q^4-1)/(q^2-1)=q^2+1
所以：q^2=4
q=±2

Answer 2

q=2；
有等差数列可知：
a5-a3=4(a3-a1);
a5+4a1=5a3
a5=a1q^4
a3=a1q^2
代入以上公式可得：q=2；

Answer 3

a5 - a3 = a1q⁴- a1q² = b12 - b4 = 8d
a3 - a1 = a1q² - a1 = b4 - b2 = 2d
a1q⁴- a1q² = 4(a1q² - a1)
q⁴- 5q² + 4 = 0
(q² - 1)(q² - 4) = 0
∵q ≠ 1
∴q = -1 或 q = 2 或 q = -2

Answer 4

由题a1=b1+d，a1q^2=b1+3d，a1q^4=b1+11d，联立得d=+-2

Answer 5

应该是正负2