如果有窮數(shù)列a1,a2,a3,…,am(m為正整數(shù))滿(mǎn)足條件a1=am,a2=am-1,…,am=a1,即ai=am-i+1(i=1,2,…,m),我們稱(chēng)其為“對(duì)稱(chēng)數(shù)列”.
例如,數(shù)列1,2,5,2,1與數(shù)列8,4,2,2,4,8都是“對(duì)稱(chēng)數(shù)列”.
(1)設(shè){bn}是7項(xiàng)的“對(duì)稱(chēng)數(shù)列”,其中b1,b2,b3,b4是等差數(shù)列,且b1=2,b4=11.依次寫(xiě)出{bn}的每一項(xiàng);
(2)設(shè){cn}是49項(xiàng)的“對(duì)稱(chēng)數(shù)列”,其中c25,c26,…,c49是首項(xiàng)為1,公比為2的等比數(shù)列,求{cn}各項(xiàng)的和S;
(3)設(shè){dn}是100項(xiàng)的“對(duì)稱(chēng)數(shù)列”,其中d51,d52,…,d100是首項(xiàng)為2,公差為3的等差數(shù)列.求{dn}前n項(xiàng)的和Sn(n=1,2,…,100).