设Sn是等差数列{an}的前n项和,若S5=a8+5,S6=a7+a9-5,则公差d=?

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设Sn是等差数列{an}的前n项和,若S5=a8+5,S6=a7+a9-5,则公差d=?
设Sn是等差数列{an}的前n项和,若S5=a8+5,S6=a7+a9-5,则公差d=?

设Sn是等差数列{an}的前n项和,若S5=a8+5,S6=a7+a9-5,则公差d=?
∵Sn是等差数列{an}的前n项和
∴a6=S6-S5
=(a7+a9-5)-(a8+5)
=a7+a9-5-a8-5
=a7+d-10
又∵a6=a1+5d,a7=a1+6d
∴a1+5d=a1+6d+d-10
即2d=10
解得:d=5

5a1+5x=4/2d=a1+7d+5
6a1+6x5/2d=a1+6d+a1+8d-5
5a1+10d=a1+7d+5
4a1+3d=5(1)
6a1+15d=2a1+14d-5
4a1+d=-5(2)
(1)-(2) 2d=10
d=5
答:公差为5

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