等差数列{an}中,a1+a4+a10+a16+a19=100,则a16-a19+a13=?

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等差数列{an}中,a1+a4+a10+a16+a19=100,则a16-a19+a13=?

a1+a4+a10+a16+a19=100
5a10=100
a10=20
a16-a19+a13
=a10+6d-a10-9d+a10+3d
=a10
=20

因为a1+a19=a4+a16=a10+a10
所以a1+a4+a10+a16+a19=5a10=100
所以a10=20
a16-a19+a13=a10+6d-a10-9d+a10+3d=a10=20

a1+a4+a10+a16+a19=100
a10+a16+a4+a1+a19=100
a10+a10+6d+a4+a1+9d+a10=100
a10+a10+a10+a10+a10=100
5a10=100
a10=20
a16-a19+a13=a10+6d-(a10+9d)+a10+3d=a10=20

∵a1+a4+a10+a16+a19=100
∴5a10=100
a10=20
∴a16-a19+a13
=a10+6d-a10-9d+a10+3d
=a10
=20