设数列{an}、{bn}都是等差数列,且a1=25,b1=75,a2+b2=100,则a37+b37等于(  ) A.0 B.37 C.100 D.-37

问题描述:

设数列{an}、{bn}都是等差数列,且a1=25,b1=75,a2+b2=100,则a37+b37等于(  )
A. 0
B. 37
C. 100
D. -37

∵数列{an}、{bn}都是等差数列,
∴数列{an+bn}也是等差数列,
∵a1+b1=25+75=100,a2+b2=100,
∴数列{an+bn}的公差为0,数列为常数列,
∴a37+b37=100
故选:C.