Sn是等差数列前n项和,Sn=16n-n平方 Tn=a1绝对值+a2绝对值.an绝对值,则Tn
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Sn是等差数列前n项和,Sn=16n-n平方 Tn=a1绝对值+a2绝对值.an绝对值,则Tn
![Sn是等差数列前n项和,Sn=16n-n平方 Tn=a1绝对值+a2绝对值.an绝对值,则Tn](/uploads/image/z/17723351-47-1.jpg?t=Sn%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E5%89%8Dn%E9%A1%B9%E5%92%8C%2CSn%3D16n-n%E5%B9%B3%E6%96%B9+Tn%3Da1%E7%BB%9D%E5%AF%B9%E5%80%BC%2Ba2%E7%BB%9D%E5%AF%B9%E5%80%BC.an%E7%BB%9D%E5%AF%B9%E5%80%BC%2C%E5%88%99Tn)
Sn=16n-n²
an=Sn - S(n-1)=16n-n²-16(n-1)+(n-1)²=17-2n,n>1
n=1时,a1=S1=15,满足上式.
∴an=17-2n
an=17-2n>0,n<17/2,即n≤8
an=17-2n<0,n>17/2,即n≥9
①n≤8时,an>0
Tn=|a1|+|a2|+|a3|+……+|an|
=a1+a2+a3+……+an
=Sn=16n-n²
②n≥9时,
Tn=|a1|+|a2|+|a3|+……+|a8|+|a9|+|a10|+……+|an|
= a1+ a2 +a3 +……+a8 - a9 - a10 - …… - an
= S8 - (a9+a10+……+an)
= S8 - [(a1+a2+……+an)-(a1+a2+……+a8)]
=S8 - (Sn-S8)
=2S8-Sn
=2×(16×8-8²) - (16n-n²)
= n²-16n+128
an=Sn - S(n-1)=16n-n²-16(n-1)+(n-1)²=17-2n,n>1
n=1时,a1=S1=15,满足上式.
∴an=17-2n
an=17-2n>0,n<17/2,即n≤8
an=17-2n<0,n>17/2,即n≥9
①n≤8时,an>0
Tn=|a1|+|a2|+|a3|+……+|an|
=a1+a2+a3+……+an
=Sn=16n-n²
②n≥9时,
Tn=|a1|+|a2|+|a3|+……+|a8|+|a9|+|a10|+……+|an|
= a1+ a2 +a3 +……+a8 - a9 - a10 - …… - an
= S8 - (a9+a10+……+an)
= S8 - [(a1+a2+……+an)-(a1+a2+……+a8)]
=S8 - (Sn-S8)
=2S8-Sn
=2×(16×8-8²) - (16n-n²)
= n²-16n+128
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