新高考數(shù)學(xué)二輪復(fù)習(xí) 易錯點(diǎn)6求數(shù)列的通項(xiàng)公式（原卷版）

易錯點(diǎn)06求數(shù)列的通項(xiàng)公式求數(shù)列通項(xiàng)公式主要以考查由遞推公式求通項(xiàng)公式與已知前n項(xiàng)和或前n項(xiàng)和與第n項(xiàng)的關(guān)系式求通項(xiàng)為重點(diǎn)，特別是數(shù)列前SKIPIF1<0項(xiàng)和SKIPIF1<0與SKIPIF1<0關(guān)系的應(yīng)用，難度為中檔題，題型為選擇填空小題或解答題第1小題，同時要注意對數(shù)列單調(diào)性與周期性問題的復(fù)習(xí)與訓(xùn)練.易錯點(diǎn)1：已知數(shù)列{an}的前n項(xiàng)和Sn與通項(xiàng)an的關(guān)系式，求an時應(yīng)注意分類討論的應(yīng)用，特別是在利用an＝Sn－Sn－1進(jìn)行轉(zhuǎn)化時，要注意分n＝1和n≥2兩種情況進(jìn)行討論，學(xué)生特別是容易忽視要檢驗(yàn)n＝1是否也適合an.?易錯點(diǎn)2：在等比數(shù)列求和公式中要注意分兩種情況q＝1和q≠1討論.易錯點(diǎn)3：在解答數(shù)列問題時，及時準(zhǔn)確地“數(shù)清”數(shù)列的項(xiàng)數(shù)是必不可少的，在數(shù)項(xiàng)數(shù)時，要把握數(shù)列的項(xiàng)的構(gòu)成規(guī)律，找準(zhǔn)數(shù)列的通項(xiàng)公式的特點(diǎn)并找準(zhǔn)項(xiàng)數(shù)．如果把數(shù)列的項(xiàng)數(shù)弄錯了，將會前功盡棄．易錯點(diǎn)4：對等差、等比數(shù)列的性質(zhì)理解錯誤。?等差數(shù)列的前n項(xiàng)和在公差不為0時是關(guān)于n的常數(shù)項(xiàng)為0的二次函數(shù)。一般地，有結(jié)論“若數(shù)列{an}的前n項(xiàng)和Sn=an2+bn+c(a，b，c∈R)，則數(shù)列{an}為等差數(shù)列的充要條件是c=0”;在等差數(shù)列中，Sm，S2m-Sm，S3m-S2m(m∈N*)是等差數(shù)列。解決這類題目的一個基本出發(fā)點(diǎn)就是考慮問題要全面，把各種可能性都考慮進(jìn)去，認(rèn)為正確的命題給以證明，認(rèn)為不正確的命題舉出反例予以駁斥。在等比數(shù)列中公比等于-1時是一個很特殊的情況，在解決有關(guān)問題時要注意這個特殊情況。??題組一:公式法已知或根據(jù)題目的條件能夠推出數(shù)列SKIPIF1<0為等差或等比數(shù)列，根據(jù)通項(xiàng)公式SKIPIF1<0或SKIPIF1<0進(jìn)行求解.1.（2019全國1理9）記為等差數(shù)列SKIPIF1<0的前n項(xiàng)和．已知SKIPIF1<0，則A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．(2018北京)設(shè)SKIPIF1<0是等差數(shù)列，且SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的通項(xiàng)公式為___．3．（2014新課標(biāo)1）已知SKIPIF1<0是遞增的等差數(shù)列，SKIPIF1<0，SKIPIF1<0是方程SKIPIF1<0的根．則SKIPIF1<0=_________.4.（2013新課標(biāo)1）已知等差數(shù)列的前項(xiàng)和滿足，．則SKIPIF1<0=_________.題組二:已知數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0的解析式，求SKIPIF1<0.5.數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，則SKIPIF1<0_________________.6.數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0__________.題組三:Sn與an的關(guān)系式法已知數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0與通項(xiàng)SKIPIF1<0的關(guān)系式，求SKIPIF1<0.7.(2015新課標(biāo)Ⅰ)SKIPIF1<0為數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和，若SKIPIF1<0，則SKIPIF1<0=________.8.(2014新課標(biāo)1)已知數(shù)列SKIPIF1<0QUOTEan的前n項(xiàng)和QUOTE，SKIPIF1<0QUOTE，其中SKIPIF1<0，則SKIPIF1<0=__________.9．(2018全國卷Ⅰ)記SKIPIF1<0為數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和，若SKIPIF1<0，則SKIPIF1<0_____．題組四:累加法當(dāng)數(shù)列SKIPIF1<0中有SKIPIF1<0，即第SKIPIF1<0項(xiàng)與第SKIPIF1<0項(xiàng)的差是個有“規(guī)律”的數(shù)時，就可以用這種方法.10.已知SKIPIF1<0，求通項(xiàng)SKIPIF1<0.11.設(shè)數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0=_______；12.（2015新課標(biāo)Ⅱ）設(shè)是數(shù)列的前n項(xiàng)和，且，，則________．1．在等差數(shù)列SKIPIF1<0中，已知SKIPIF1<0，則SKIPIF1<0（）A．4 B．8 C．3 D．62．已知等差數(shù)列SKIPIF1<0，公差為SKIPIF1<0，且SKIPIF1<0、SKIPIF1<0、SKIPIF1<0成等比數(shù)列，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．若數(shù)列SKIPIF1<0是等差數(shù)列，a1=1，SKIPIF1<0，則a5=（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知數(shù)列SKIPIF1<0是公比為正數(shù)的等比數(shù)列，SKIPIF1<0是其前SKIPIF1<0項(xiàng)和，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（）A．31 B．63 C．127 D．2555．設(shè)數(shù)列SKIPIF1<0為等比數(shù)列，若SKIPIF1<0，SKIPIF1<0，則數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知等比數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．設(shè)數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．若數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．若數(shù)列SKIPIF1<0的前n項(xiàng)和SKIPIF1<0(n∈N*)，則SKIPIF1<0=（）A．20 B．30 C．40 D．5010．已知數(shù)列