等差数列{an}的前n项和为Sn,且a10=30,a20=50 (1)求通项an(2)若Sn=242求n

问题描述:

等差数列{an}的前n项和为Sn,且a10=30,a20=50 (1)求通项an(2)若Sn=242求n

由题意可知步长为(50-30)/10=2,那么a1=30-(10-1)*2=12
(1)an=a1+(n-1)*2=12+(n-1)*2
(2)a1+an=a2+a(n-1)=a3+a(n-2)=...
Sn=a1+a2+a3+...+an
=(a1+an)*(n/2) => (12+(12+(n-1)*2))*(n/2)=242
==>n=11或-22(舍去)