设{an}是等差数列,{bn}是等比数列,记{an}{bn}的前n项和分别为Sn,Tn若a3=b3,a4=b4,且(S5-S3)/(T4-T2)=5,则(a5+a3)/(b5+b3)=?
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设{an}是等差数列,{bn}是等比数列,记{an}{bn}的前n项和分别为Sn,Tn若a3=b3,a4=b4,且(S5-S3)/(T4-T2)=5,则(a5+a3)/(b5+b3)=?设{an}是等
设{an}是等差数列,{bn}是等比数列,记{an}{bn}的前n项和分别为Sn,Tn若a3=b3,a4=b4,且(S5-S3)/(T4-T2)=5,则(a5+a3)/(b5+b3)=?
设{an}是等差数列,{bn}是等比数列,记{an}{bn}的前n项和分别为Sn,Tn若a3=b3,a4=b4,且(S5-S3)/(T4-T2)=5,则(a5+a3)/(b5+b3)=?
设{an}是等差数列,{bn}是等比数列,记{an}{bn}的前n项和分别为Sn,Tn若a3=b3,a4=b4,且(S5-S3)/(T4-T2)=5,则(a5+a3)/(b5+b3)=?
设等差数列的等差为d,等比数列的等比是q
则
a3=b3
a4-d=b4/q
又∵a4=b4
∴a4-d=a4/q
a4-a4/q=d
∵(S5-S3)/(T4-T2)=5
∴(a5+a4)/(b4+b3)=(a4+d+a4)/(a4+b4/q)=(2a4+d)/(a4+a4/q)=5
即(2a4+a4-a4/q)/(a4+a4/q)=5
左边可以分子分母同时除以a4,即
(2+1-1/q)/(1+1/q)=5
左边分数上下同时乘以q
(3q-1)/(q+1)=5
3q-1=5q+5
-1-5=2q
q=-3
根据等差中项可知,a5+a3=2a4
(a5+a3)/(b5+b3)=2a4/(b4*q+b4/q)=2a4/(-3a4-a4/3)=2/(-10/3)=-3/5
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