题目如图,AP1AP_{1}AP1为△ABC\triangle ABC△ABC的中线,AP2AP_{2}AP2为△AP1C\triangle AP_{1}C△AP1C的中线,AP3AP_{3}AP3为△AP2C\triangle AP_{2}C△AP2C的中线,…\ldots…,按此规律,APn+1AP_{n+1}APn+1为△APnC\triangle AP_{n}C△APnC的中线,若△ABP1\triangle ABP_{1}△ABP1的面积为111,则△APnC\triangle AP_{n}C△APnC的面积为( )A.2n2^{n}2nB.2−n2^{-n}2−nC.2n−12^{n-1}2n−1D.21−n2^{1-n}21−n知识点:旋转的性质章节:未标注