已知数列【an】是等差数列,Sn是其前n项的和,求证S6,S12-S6,S18-S12也成等差数列.

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已知数列【an】是等差数列,Sn是其前n项的和,求证S6,S12-S6,S18-S12也成等差数列.已知数列【an】是等差数列,Sn是其前n项的和,求证S6,S12-S6,S18-S12也成等差数列.

已知数列【an】是等差数列,Sn是其前n项的和,求证S6,S12-S6,S18-S12也成等差数列.
已知数列【an】是等差数列,Sn是其前n项的和,求证S6,S12-S6,S18-S12也成等差数列.

已知数列【an】是等差数列,Sn是其前n项的和,求证S6,S12-S6,S18-S12也成等差数列.
an = a1+(n-1)d
Sn =(2a1+(n-1)d)n/2
S18-S12 = (2a1+17d)9 - (2a1+11d)6
= 6a1+87d
S12-S6 = (2a1+11d)6 - (2a1+5d)3
=6a1 +51d
S6 = (2a1+5d)3 = 6a1+15d
(S18-S12) = 6a1+87d -(6a1 +51d) =36d
S12-S6 =6a1 +51d - (6a1+15d) = 36d = (S18-S12)
=>S6,S12-S6,S18-S12成等差数列.

第一项为a,等差b
S6=6a+15b
S12=12a+66b
s18=18a+153b=3*(6a+51b)=3S12-3S6
2S12-2S6=S18-S12+S6
S6,S12-S6,S18-S12也成等差数列；

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