设等差数列｛AN｝的前N项和为SN,6S5-5S3=5则A4=?

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设等差数列｛AN｝的前N项和为SN,6S5-5S3=5则A4=?
设等差数列｛AN｝的前N项和为SN,6S5-5S3=5则A4=?

设等差数列｛AN｝的前N项和为SN,6S5-5S3=5则A4=?
s5=a1+a2+a3+a4+a5=5a3
s3=a1+a2+a3=3a2
6S5-5S3=5
6*5a3-5*3a2=5
30a3-15a2=5
6a3-3a2=1
6(a2+d)-3a2=1
6a2+6d-3a2=1
3a2+6d=1
a2+2d=1/3
a4=a2+2d=1/3

Sn=na1+n*(n-1)*d/2
∴S5=5a1+10d,S3=3a1+3d
∴6S5-5S3=30a1+60d-15a1-15d
=15a1+45d=5
∴a4=a1+3d=1/3

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