2.等比數(shù)列的有關(guān)公式
(1)通項(xiàng)公式:an=a1qn-1.
(2)前n項(xiàng)和公式:
Sn=
3.等比數(shù)列的性質(zhì)
(1)通項(xiàng)公式的推廣:an=am·qn-m(m,n∈N+).
(2)對任意的正整數(shù)m,n,p,q,若m+n=p+q,則am·an=ap·aq.
特別地,若m+n=2p,則am·an=a.
(3)若等比數(shù)列前n項(xiàng)和為Sn,則Sm,S2m-Sm,S3m-S2m仍成等比數(shù)列,即(S2m-Sm)2=Sm(S3m-S2m)(m∈N+,公比q≠-1).
(4)數(shù)列{an}是等比數(shù)列,則數(shù)列{pan}(p≠0,p是常數(shù))也是等比數(shù)列.
(5)在等比數(shù)列{an}中,等距離取出若干項(xiàng)也構(gòu)成一個等比數(shù)列,即an,an+k,an+2k,an+3k,…為等比數(shù)列,公比為qk.