一道英语数学题The first term and common difference of an arithmetic
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一道英语数学题
The first term and common difference of an arithmetic sequence are integers.The sum of the first n terms of this sequence is Sn.
(1)If a11=0,S14=98,find the general term of the sequence.
(2)If a1>=6,a11>=0,S14
The first term and common difference of an arithmetic sequence are integers.The sum of the first n terms of this sequence is Sn.
(1)If a11=0,S14=98,find the general term of the sequence.
(2)If a1>=6,a11>=0,S14
(1)
since a11=0 so a1+10d=0…………………………(1)
S14=98 so (2a1+13d)*14/2=98 so 2a1+13d=14 (2)
2(1)-(2)=7d=-14 d=-2 then a1=20
So that the general term of the sequence is an=22-2n
(2)
a1>=6
a11=a1+10d>0
(2a1+13d)*14/2
since a11=0 so a1+10d=0…………………………(1)
S14=98 so (2a1+13d)*14/2=98 so 2a1+13d=14 (2)
2(1)-(2)=7d=-14 d=-2 then a1=20
So that the general term of the sequence is an=22-2n
(2)
a1>=6
a11=a1+10d>0
(2a1+13d)*14/2
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