若等比数列{an}中，a3=3，a5=27，则此数列的公比为（ ）A．3B．-3C．±3D．±
\u82e5\u7b49\u6bd4\u6570\u5217{an}\u4e2d\uff0ca3=3,a5=9,\u5219\u6b64\u6570\u5217\u7684\u516c\u6bd4\u4e3a\u591a\u5c11\uff1fa5=a3q^2 a3=3,a5=9
\u6240\u4ee5q=\u221a3 (\u7531\u9898\u77e5\u9053a5>a3,\u6240\u4ee5\u6b64\u7b49\u6bd4\u6570\u5217\u662f\u9012\u589e\u6570\u5217\u3002\u6545\u820d\u53bb-\u221a3.\uff09
\u6240\u4ee5\u516c\u6bd4\u4e3a\u221a3
a1=1
a1*a2/a1*a3/a2*a4/a3*a5/a4=1^6*q^(1+2+3+4)
\u5373a5=1*q^10=(-\u221a2)^10=2^5=32
\u8fd9\u662f\u6211\u5728\u9759\u5fc3\u601d\u8003\u540e\u5f97\u51fa\u7684\u7ed3\u8bba\uff0c
\u5982\u679c\u80fd\u5e2e\u52a9\u5230\u60a8\uff0c\u5e0c\u671b\u60a8\u4e0d\u541d\u8d50\u6211\u4e00\u91c7\u7eb3~\uff08\u6ee1\u610f\u56de\u7b54\uff09
\u5982\u679c\u4e0d\u80fd\u8bf7\u8ffd\u95ee\uff0c\u6211\u4f1a\u5c3d\u5168\u529b\u5e2e\u60a8\u89e3\u51b3\u7684~
\u7b54\u9898\u4e0d\u6613\uff0c\u5982\u679c\u60a8\u6709\u6240\u4e0d\u6ee1\u613f\u610f\uff0c\u8bf7\u8c05\u89e3~
由a3=3，a5=27，得q2＝
| a5 |
| a3 |
| 27 |
| 3 |
∴q=±3．
故选C．
绛旓細a3=a1*q²锛宻3=a1*(1-q³)鑱旂珛鏂圭▼寮忚В寰楋細q=1锛宎1=3鎴杚=-1锛2锛宎1=12 鎵浠锛宎n=12*(-1锛2)鐨刵-1娆℃柟锛孲n=12*(1-(-1锛2)鐨刵娆℃柟)锛忥紙1-锛-1锛2锛夛級鎴an=3锛Sn=3*n
绛旓細瑙ｏ細璁惧叕宸负d锛屽垯d鈮0 a1銆乤5銆乤13鎴绛夋瘮鏁板垪锛鍒 a5²=a1脳a3 (a3+2d)²=(a3-2d)a3 a3=3浠ｅ叆锛屾暣鐞嗭紝寰 2d²+9d=0 d(2d+9)=0 d=0(鑸嶅幓)鎴杁=-9/2 a1=a3-2d=3-2脳(-9/2)=12 S20=20a1+20脳19脳d/2 =20脳12+20脳19脳(-9/2)/2 =-615 ...
绛旓細1) 璁惧叕宸负d a1=a3-2d=3-2d a7=a3+4d=3+4d s7=(a1+a7)脳7梅2 =锛3-2d+3+4d锛壝7/2 =(6+2d)脳7/2 =7(d+3)=28 d+3=4 d=1 2)b1=a2=a3-d=3-1=2 b2=a4=a3+d=3+1=4 鎵浠 鍏瘮涓4梅2=2 bn鐨勫墠n椤瑰拰=b1(1-2^n)/(1-2)=2(2^n-1)=2^(n+1)-2...
绛旓細a5²=a1脳a13 a1²+8a1d+16d²=a1²+12a1d a1=4d a3=a1+2d=6d=3 d=0.5 a1=2 a20=a1+19d=2+19脳0.5=11.5 S20=锛坅1+a20锛壝20梅2=135
绛旓細-729=27q^3 q^3=-27 q=-3 宸茬煡绛夋瘮鏁板垪锝沘n锝濅腑锛鑻3=3锛宎10=384锛屽垯鏁板垪閫氶」鍏紡an=鈥斺攁10=a3q^7 384=3q^7 q^7=128 q^7=2^7 q=2 a3=a1q^2 3=a1*2^2 a1=3/4 an=a1q^(n-1)=3/4*2^(n-1)=3*2^(-2)*2^(n-1)=3*2^(n-3)鑻ョ瓑姣旀暟鍒楋經an锝濅腑锛鑻ラ...
绛旓細a1+a2+a3=S3 鍗3/锛2q^2锛+3/2q+3/2=9/2 鍖栫畝寰楋紝2q^2-q-1=0 瑙ｅ緱q= -1/2 鎴 1 锛堝彲鑳藉師棰樿繕鏈夊叾浠栭檺瀹氭潯浠讹紝鎵浠ヤ娇寰梣涓嶄负-1/2锛屼粎涓1锛塹=1鏃讹紝a1=3/2
绛旓細a5=a3 q²q=卤1/2 (1)褰搎=1/2鏃锛宎n=32脳(1/2)^(n锛3)=2^(8锛峮)褰搎=锛1/2鏃讹紝an=32脳(锛1/2)^(n锛3)=(锛1)^(n锛3) 脳 2^(8锛峮)(2)an=2^(8锛峮)=2^(锛1)8锛峮=锛1锛宯=9 an=(锛1)^(n锛3) 2^(8锛峮)=2^(锛1)n锛3 涓哄伓鏁帮紝8锛峮=锛1...
绛旓細(1)S3-S1=S2-S3 a1+a2+a3-a1=a1+a2-a1-a2-a3 a2+2a3=0 a2+2a2q=0 q=-1/2 (2)a1-a3=3 a1-a1/4=3 a1=4 Sn=a1(1-q^n)/(1-q)=4[1-(-1/2)^n]/(3/2)=8[1-(-1/2)^n]/3
绛旓細a(1)=1 a(2)=a(1+1)=3S(1)=3*1=3 a(3)=a(2+1)=3S(2)=3*(1+3)=12 a(4)=a(3+1)=3S(3)=3*(1+3+12)=48 a(5)=a(4+1)=3S(4)=3*(1+3+12+48)=192 a(6)=a(5+1)=3S(5)=3*(1+3+12+48+192)=768 S(6)=768+192+48+12+3+1=1024 ...
绛旓細姝ｅ鍓嶉潰鎵婢勬竻鐨绛夋瘮鏁板垪瀹氫箟鍜岀瓑姣斾腑椤瑰畾涔夋墍璁诧紝绗簩涓緥棰樻樉鐒舵槑纭a3,a7鏄瓑姣旀暟鍒楃殑椤癸紝鏁呭畠蹇呴』鏈嶄粠绛夋瘮鏁板垪鐨勫畾涔夈傛垜瑙夊緱浣犺鈥渁3+a7=11/3,鎵浠3>0,a7>0,鍒檃5鍙栧间负鏍瑰彿3鈥濆苟涓嶅Ε褰擄紝搴旇杩欐牱鍋氾紝鍏堣В3x²-11x+9=0寰梮1=3锛寈2=1锛岃繖鏃舵湁涓ょ鎯呭喌锛宎3=3锛宎7=1鎴栬卆3=1,...
