已知等比数列的公比是1/2,且a1+a3+a5+……+a99=60,求a1+a2+a3+……+a100
问题描述：
已知等比数列的公比是1/2,且a1+a3+a5+……+a99=60,求a1+a2+a3+……+a100
答
Sn = (a1 -a1 * q^n)/(1 - q)
60 = a1 -a1 * (1/4)^50 /( 3/4)
解得：
a1 = 45* 4^50 / (4^50 -1)
Sn = [a1 - a1* (1/2)^100] /(1 - 1/2)
=2* a1*(1 - 1/2^100)
= 2* 45* 4^50 /(4^50 -1)
= 90
答
a2=a1 /2
a4=a3 /2
a6=a5 /2
.....
a100=a99 /2
所有式子相加
a2+a4+a6+.....+a100=(a1+a3+a5+....+a99)/2=30
因a1+a3+a5+……+a99=60
所以a1+a2+a3+……+a100=90
答
设公比是q=1/2.
a2+a4+a6……+a100
=(a1*q)+(a3*q)+(a5*q)+……+(a99*q)
=(a1+a3+a5+…+a99)*q
=60×1/2
=30
a1+a2+a3+…+a99+a100
=(a1+a3+a5+…+a99)+ (a2+a4+a6……+a100)
=60+30
=90