设数列{an}和{bn}都是等差数列,其中a1=25,b1=75,且a100+b100=100,则数列{an+bn}的前100项之和是(  ) A.1000 B.10000 C.1100 D.11000

问题描述:

设数列{an}和{bn}都是等差数列,其中a1=25,b1=75,且a100+b100=100,则数列{an+bn}的前100项之和是(  )
A. 1000
B. 10000
C. 1100
D. 11000

∵{an}、{bn}都是等差数列,
∴{an+bn}是等差数列,
∵a1=25,b1=75,a100+b100=100,
∴a1+b1+a100+b100=200,
∴S100=

100(a1+b1+a100+b100)
2
=10000
故选B