等差数列{an}的前n项和为Sn,S15=225,S9-S5=54,求通项

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等差数列{an}的前n项和为Sn,S15=225,S9-S5=54,求通项
等差数列{an}的前n项和为Sn,S15=225,S9-S5=54,求通项

等差数列{an}的前n项和为Sn,S15=225,S9-S5=54,求通项
S15=15a1+1/2*15*14*d=225
即a1+7d=15.(1)
S9-S5=(9a1+36d)-(5a1+10d)=4a1+26d=54
即2a1+13d=27.(2)
(1)(2)得a1=-6,d=3.
故an=a1+(n-1)d=-6+3(n-1)=3n-9

S15=15a1+15*14d/2=15a1+105d=225
a1+7d=15 1
S9-S5=9a1+9*8d/2-(5a1+5*4d/2)
=9a1+36d-5a1-10d
=4a1+26d=54
2a1+13d=27 2
1式*2-2式得
d=3 3
3式代入1式得
a1=-6
an=a1+(n-1)d
=-6+(n-1)*3
=3n-9

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