Question

已知等差数列〖an〗满足：a3=7,a5+a7=26，{an}的前n项和为sn (1)求an及sn

Answer 1

设an=a1+(n-1)d,
a3=7,a5+a7=26
a3+a5+a7=33
3a5=33
a5=11
a5-a3=2d=11-7=4
d=2，a1=3
an=3+(n-1)2=2n+1
Sn=(3+2n+1)n/2=n^2+2n
中间使用了：an-am=(n-m)d

Answer 2

等差数列的话，a3=a1+2d=7,a5=a7=2a1+10d=26,姐方程组得d=2,a1=3,所以an=1+2n
sn=n(a1+an)/2=n^2+2n

Answer 3

a5+a7=2a6=26,a6=13,a3=7,d=(a6-a3)/3=2,an=a3+2(n-3)=2n+1..
sn=n(n+2);...