[小題體驗(yàn)]
1.?dāng)?shù)列-1,,-,,…的一個(gè)通項(xiàng)公式是________.
解析:-1=-,數(shù)列1,4,9,16,…對(duì)應(yīng)通項(xiàng)n2,數(shù)列1,3,5,7,…對(duì)應(yīng)通項(xiàng)2n-1,數(shù)列-1,1,-1,1,…對(duì)應(yīng)通項(xiàng)(-1)n,故an=(-1)n·.
答案:an=(-1)n·
2.已知數(shù)列滿足an=4an-1+3,且a1=0,則a5=________.
解析:a2=4a1+3=3,a3=4a2+3=15,a4=4a3+3=63,a5=4a4+3=255.
答案:255
3.?dāng)?shù)列{an}的通項(xiàng)公式為an=-n2+9n,則該數(shù)列第________項(xiàng)最大.
答案:4或5
4.若數(shù)列的前n項(xiàng)和Sn=n2+3n,則=________.
解析:∵數(shù)列的前n項(xiàng)和Sn=n2+3n,
∴a1+a2+a3=S3=32+3×3=18,
∵a4+a5+a6=S6-S3=36,∴=2.
答案:2
1.易混項(xiàng)與項(xiàng)數(shù)的概念,數(shù)列的項(xiàng)是指數(shù)列中某一確定的數(shù),而項(xiàng)數(shù)是指數(shù)列的項(xiàng)對(duì)應(yīng)的位置序號(hào).
2.在利用數(shù)列的前n項(xiàng)和求通項(xiàng)時(shí),往往容易忽略先求出a1,而是直接把數(shù)列的通項(xiàng)公式寫成an=Sn-Sn-1的形式,但它只適用于n≥2的情形.
[小題糾偏]
1.已知數(shù)列{an}的前n項(xiàng)和Sn=2n-3,則數(shù)列{an}的通項(xiàng)公式是________________.