若数列an满足a1等于1 Sn等于二分之一(3n-1)则an等于多少

问题描述:

若数列an满足a1等于1 Sn等于二分之一(3n-1)则an等于多少


当sn=1/2(3n-1)
当n=1时,a1=1
当n>=2时
an=sn-s(n-1)=1/2(3n-1)-1/2[3(n-1)-1]
=1/2(3n-1)-1/2(3n-4)
=1/2(3n-1-3n+4)
=1/2×3
=3/2

an={1n=1
{3/2 n>=2