高中數(shù)學(xué)人教A版必修五 第二章 數(shù)列 學(xué)業(yè)分層測評12 含答案

1、人教版高中數(shù)學(xué)必修精品教學(xué)資料學(xué)業(yè)分層測評（十二）(建議用時：45分鐘)學(xué)業(yè)達(dá)標(biāo)一、選擇題12與2的等比中項(xiàng)是()a1b1c±1d2【解析】2與2的等比中項(xiàng)為g±±1,故選c.【答案】c2在等比數(shù)列an中,a2 0168a2 015,則公比q的值為()a2b3c4d8【解析】因?yàn)閍2 0168a2 015,所以a1q2 0158a1·q2 014,解得q8.【答案】d3已知一等比數(shù)列的前三項(xiàng)依次為x,2x2,3x3,那么13是此數(shù)列的()a第2項(xiàng)b第4項(xiàng)c第6項(xiàng)d第8項(xiàng)【解析】由x,2x2,3x3成等比數(shù)列,可知(2x2)2x(3x3),解得x1或4,又

2、當(dāng)x1時,2x20,這與等比數(shù)列的定義相矛盾x4,該數(shù)列是首項(xiàng)為4,公比為的等比數(shù)列,其通項(xiàng)an4n1,由4n113,得n4.【答案】b4已知a,b,c,d成等比數(shù)列,且曲線yx22x3的頂點(diǎn)坐標(biāo)是(b,c),則ad等于()a3b2c1d2【解析】由yx22x3(x1)22,得b1,c2.又a,b,c,d成等比數(shù)列,即a,1,2,d成等比數(shù)列,所以d4,a,故ad4×2.【答案】b5(2015·全國卷)已知等比數(shù)列an滿足a13,a1a3a521,則a3a5a7()a21b42c63d84【解析】a13,a1a3a521,33q23q421,1q2q47,解得q22或q23

3、(舍去)a3a5a7q2(a1a3a5)2×2142.故選b.【答案】b二、填空題6已知等比數(shù)列an中,a12,且a4a64a,則a3 .【解析】設(shè)等比數(shù)列an的公比為q,由已知條件得a4·aq4.q4,q2,a3a1q22×1.【答案】17已知等比數(shù)列an中,a33,a10384,則該數(shù)列的通項(xiàng)an .【解析】由已知得q712827,故q2.所以ana1qn1a1q2·qn3a3·qn33×2n3.【答案】3×2n38在等比數(shù)列an中,an>0,且a1a21,a3a49,則a4a5 .【解析】由已知a1a21,a3a

4、49,q29.q3(q3舍),a4a5(a3a4)q27.【答案】27三、解答題9在各項(xiàng)均為負(fù)的等比數(shù)列an中,2an3an1,且a2·a5.(1)求數(shù)列an的通項(xiàng)公式；(2)是否為該數(shù)列的項(xiàng)？若是,為第幾項(xiàng)？【解】(1)因?yàn)?an3an1,所以,數(shù)列an是公比為的等比數(shù)列,又a2·a5,所以a53,由于各項(xiàng)均為負(fù),故a1,ann2.(2)設(shè)an,則n2,n24,n6,所以是該數(shù)列的項(xiàng),為第6項(xiàng)10數(shù)列an,bn滿足下列條件：a10,a21,an2,bnan1an.(1)求證：bn是等比數(shù)列；(2)求bn的通項(xiàng)公式【解】(1)證明：2an2anan1,.bn是等比數(shù)列(2)

5、b1a2a11,公比q,bn1×n1n1.能力提升1已知等比數(shù)列an中,各項(xiàng)都是正數(shù),且a1,a3,2a2成等差數(shù)列,則等于()a.1b32c32d23【解析】設(shè)等比數(shù)列an的公比為q,由于a1,a3,2a2成等差數(shù)列,則2a12a2,即a3a12a2,所以a1q2a12a1q.由于a10,所以q212q,解得 q1±.又等比數(shù)列an中各項(xiàng)都是正數(shù),所以q>0,所以q1.所以32.【答案】322(2015·全國卷)已知等比數(shù)列an滿足a1,a3a54(a41),則a2()a2b1c.d【解析】法一a3a5a,a3a54(a41),a4(a41),a4a440

6、,a42.又q38,q2,a2a1q×2,故選c.法二a3a54(a41),a1q2·a1q44(a1q31),將a1代入上式并整理,得q616q3640,解得q2,a2a1q,故選c.【答案】c3(2015·浙江高考)已知an是等差數(shù)列,公差d不為零若a2,a3,a7成等比數(shù)列,且2a1a21,則a1 ,d .【解析】a2,a3,a7成等比數(shù)列,aa2a7,(a12d)2(a1d)(a16d),即2d3a10.又2a1a21,3a1d1.由解得a1,d1.【答案】14已知數(shù)列an滿足a11,an12an1.(1)求證：數(shù)列an1是等比數(shù)列；(2)求an的表達(dá)式. 【導(dǎo)學(xué)號：05920070】【解】(1)證明：an12an1