设Sn是等差数列{an}的前n项和,已知a2=3,a6=11,则S7=?

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设Sn是等差数列{an}的前n项和,已知a2=3,a6=11,则S7=?
设Sn是等差数列{an}的前n项和,已知a2=3,a6=11,则S7=?

设Sn是等差数列{an}的前n项和,已知a2=3,a6=11,则S7=?
a2=3,a6=a2+4d=11,得d=2
a1=1 a7=13
S7=7（a1+a7)/2
S7=49

d=(a6-a2)/(6-2)=2
a4=a2+2d=7
a1+a7=2a4
a2+a6=2a4
a3+a5=2a4
S7=7a4=7*7=49

S7=49

由题知，
Sn是等差数列{an}的前n项和
S7=(a1+a7)*7/2
=(a2+a6)*7/2
=(3+11)*7/2
=49

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