等差数列{a下标n}中,若a1005+a1006+a1007=6,则该数列前2011项的和为4022,

题目

等差数列{a下标n}中,若a1005+a1006+a1007=6,则该数列前2011项的和为4022,

答案

a1005+a1006+a1007=a1005+a1005+d+a1006+2d=3a1005+3d=6a1005+d=2a1+1004d+d=2a1+1005d=2S2011=2011a1+2011*2010*d/2=2011a1+1005*2011d=2011(a1+1005d)=2011*2=4022