高中數(shù)學(xué) 2.4 等比數(shù)列知識(shí)表格素材 新人教必修5

1.等比數(shù)列與等差數(shù)列的區(qū)別與聯(lián)系不同點(diǎn)等差數(shù)列（1）若{an}為正項(xiàng)等比數(shù)列,則{logaan}（a>0且a≠1）為等差數(shù)列；（2）若{an}為等差數(shù)列，則{}為等比數(shù)列（b≠0）.（1）都強(qiáng)調(diào)每一項(xiàng)與前一項(xiàng)的關(guān)系；（2）差或比結(jié)果都必須是常數(shù)；（3）數(shù)列都可以由a1，d或a1，q確定.等比數(shù)列相同點(diǎn)聯(lián)系（1）強(qiáng)調(diào)每一項(xiàng)與前一項(xiàng)的比值；（2）a1與q均不為零.（1）強(qiáng)調(diào)每一項(xiàng)與前一項(xiàng)的差；（2）a1和d可以為零..2.等比數(shù)列的前n項(xiàng)和等比數(shù)列前n項(xiàng)和公比適用公式q=1q≠1.3.等差、等比數(shù)列的判定方法定義法中項(xiàng)法an+1-an=d(d為常數(shù))方法分類等差數(shù)列等比數(shù)列2an+1＝an+an+2（n∈N*）.4.等差、等比數(shù)列的性質(zhì)條件等差數(shù)列m，n，p，q∈N*且m+n=p+q項(xiàng)數(shù)成等差數(shù)列等比數(shù)列am+an=ap+aq

am?an=ap?aq對(duì)應(yīng)項(xiàng)仍成等差數(shù)列對(duì)應(yīng)項(xiàng)仍成等比數(shù)列m∈N*，Sm為前n項(xiàng)和Sm≠0Sm,S2m-Sm,S3m-S2m,…仍成等差數(shù)列Sm,S2m-Sm,S3m-S2m,…仍成等比數(shù)列規(guī)定：1.S奇、S偶分別為數(shù)列中所有奇數(shù)項(xiàng)的和與所有偶數(shù)項(xiàng)的和2..條件等差數(shù)列項(xiàng)數(shù)為奇數(shù)時(shí)等比數(shù)列S奇-S偶＝a中項(xiàng)數(shù)為偶數(shù)時(shí).等差數(shù)列{an}等比數(shù)列{an}定義⑴通項(xiàng)公式⑵推導(dǎo)方法性質(zhì)前n項(xiàng)和Sn⑴公式⑵推導(dǎo)方法an+1-an=d(常數(shù))an+1／an=q(不為零的常數(shù))an=a1+(n–1)dan-am=(n–m)dan=a1qn-1an／am=qn-m①歸納猜想驗(yàn)證法②首尾相咬累加法①歸納猜想驗(yàn)證法②首尾相咬累乘法若m+n=r+s,m，n，r，s∈N*則am+an=ar+as若m+n=r+s,m，n，r，s∈N*則am·an=ar·as當(dāng)q＝1時(shí)Sn=