设{an}是公差为2的等差数列,且S100=100,求a4+a8+a12+……+a100

问题描述:

设{an}是公差为2的等差数列,且S100=100,求a4+a8+a12+……+a100

an}是公差为2的等差数列
S100=(a1+a100)x50=100
=>a1+a100=2
=>a4-6+a100=2
=>a4+a100=8
a4+a8+a12+……+a100=(a4+a100)x25/2=4x25=100