(1)Q型车每月的销售量{an}是以首项a1=a,公比q=1+1%=1.01的等比数列; 前n个月的销售总量Sn==100a(1.01n-1)(n∈N*,且n≤24). (2)∵Sn-Tn=100a(1.01n-1)-228a(1.012n-1)=100a(1.01n-1)-228a(1.01n-1)(1.01n+1)=-228a(1.01n-1)•(1.01n+). 又1.01n-1>0,1.01n+>0,∴Sn<Tn. (3)记Q、R两款车第n个月的销量分别为an和bn, 则an=a×1.01n-1. 当n≥2时,bn=Tn-Tn-1=228a(1.012n-1)-228a(1.012n-2-1)=228a×(1.012-1)×1.012n-2=4.5828a1.012n-2. b1=4.5828a(或228×0.0201a),显然20%×b1<a1. 当n≥2时,若an<20%×bn, 即a×1.01n-1<×4.5828a×1.012n-2, 1.012(n-1)>×1.01n-1,1.01n-1>≈1.09,n-1>≈8.66. ∴n≥10,即从第10个月开始,Q型车月销售量小于R型车月销售量的20%. |