µÈ±ÈÊýÁоµäÀýÌâ͸Îö
ÀàÐÍÒ»£ºµÈ±ÈÊýÁеÄͨÏʽ
Àý1£®µÈ±ÈÊýÁÐ{an}ÖУ¬a1?a9?64, a3?a7?20,Çóa11.
˼·µã²¦£ºÓɵȱÈÊýÁеÄͨÏʽ£¬Í¨¹ýÒÑÖªÌõ¼þ¿ÉÁгö¹ØÓÚa1ºÍqµÄ¶þÔª·½³Ì×飬½â³öa1ºÍq£¬¿ÉµÃa11£»»ò×¢Ò⵽ϱê1?9?3?7£¬¿ÉÒÔÀûÓÃÐÔÖÊ¿ÉÇó³ö
a3¡¢a7£¬ÔÙÇóa11.
×ܽáÉý»ª£º ¢ÙÁз½³Ì£¨×飩Çó½âÊǵȱÈÊýÁеĻù±¾·½·¨£¬Í¬Ê±ÀûÓÃÐÔÖÊ¿ÉÒÔ¼õÉÙ¼ÆËãÁ¿£» ¢Ú½âÌâ¹ý³ÌÖоßÌåÇó½âʱ£¬ÒªÉè·¨½µ´ÎÏûÔª£¬³£³£ÕûÌå´úÈëÒÔ´ï½µ´ÎÄ¿µÄ£¬¹Ê½Ï¶à±äÐÎÒªÓóý·¨£¨³ýʽ²»ÎªÁ㣩.
¾ÙÒ»·´Èý£º
¡¾±äʽ1¡¿{an}ΪµÈ±ÈÊýÁУ¬a1=3£¬a9=768£¬Çóa6¡£
¡¾±äʽ2¡¿{an}ΪµÈ±ÈÊýÁУ¬an£¾0£¬ÇÒa1a89=16£¬Çóa44a45a46µÄÖµ¡£
¡¾±äʽ3¡¿ÒÑÖªµÈ±ÈÊýÁÐ{an}£¬Èôa1?a2?a3?7£¬a1a2a3?8£¬Çóan¡£ ÀàÐͶþ£ºµÈ±ÈÊýÁеÄǰnÏîºÍ¹«Ê½
Àý2£®ÉèµÈ±ÈÊýÁÐ{an}µÄǰnÏîºÍΪSn£¬ÈôS3+S6=2S9£¬ÇóÊýÁеĹ«±Èq. ½âÎö£ºÈôq=1£¬ÔòÓÐS3=3a1£¬S6=6a1£¬S9=9a1.
Òòa1¡Ù0£¬µÃS3+S6¡Ù2S9£¬ÏÔÈ»q=1ÓëÌâÉèì¶Ü£¬¹Êq¡Ù1.
a1(1?q3)a1(1?q6)2a1(1?q9)??ÓÉS3?S6?2S9µÃ£¬£¬
1?q1?q1?qÕûÀíµÃq3(2q6-q3-1)=0£¬
ÓÉq¡Ù0£¬µÃ2q6-q3-1=0£¬´Ó¶ø(2q3+1)(q3-1)=0£¬
341Òòq¡Ù1£¬¹Êq??£¬ËùÒÔq??¡£
223
3¾ÙÒ»·´Èý£º
11¡¾±äʽ1¡¿ÇóµÈ±ÈÊýÁÐ1,,,?µÄǰ6ÏîºÍ¡£
39¡¾±äʽ2¡¿ÒÑÖª£º{an}ΪµÈ±ÈÊýÁУ¬a1a2a3=27£¬S3=13£¬ÇóS5.
¡¾±äʽ3¡¿ÔڵȱÈÊýÁÐ{an}ÖУ¬a1?an?66£¬a2?an?1?128£¬Sn?126£¬ÇónºÍ ÀàÐÍÈý£ºµÈ±ÈÊýÁеÄÐÔÖÊ
Àý3. µÈ±ÈÊýÁÐ{an}ÖУ¬Èôa5?a6?9,Çólog3a1?log3a2?...?log3a10. ¾ÙÒ»·´Èý£º
¡¾±äʽ1¡¿ÕýÏîµÈ±ÈÊýÁÐ{an}ÖУ¬Èôa1¡¤a100=100; Ôòlga1+lga2+¡¡+lga100=_____________.
827¡¾±äʽ2¡¿ÔÚºÍÖ®¼ä²åÈëÈý¸öÊý£¬Ê¹ÕâÎå¸öÊý³ÉµÈ±ÈÊýÁУ¬Ôò²åÈëµÄÈý
32¸öÊýµÄ³Ë»ýΪ________¡£
ÀàÐÍËÄ£ºµÈ±ÈÊýÁÐǰnÏîºÍ¹«Ê½µÄÐÔÖÊ
Àý4£®ÔڵȱÈÊýÁÐ{an}ÖУ¬ÒÑÖªSn?48£¬S2n?60£¬ÇóS3n¡£
˼·µã²¦£ºµÈ²îÊýÁÐÖÐÒ²ÓÐÀàËÆµÄÌâÄ¿£¬ÎÒÃÇÈÔÈ»²ÉÓõȲîÊýÁеĽâ¾ö°ì·¨£¬¼´µÈ±ÈÊýÁÐÖÐǰkÏîºÍ£¬µÚ2¸ökÏîºÍ£¬µÚ3¸ökÏîºÍ£¬¡¡£¬µÚn¸ökÏîºÍÈÔÈ»³ÉµÈ±ÈÊýÁС£
¾ÙÒ»·´Èý£º
¡¾±äʽ1¡¿µÈ±ÈÊýÁÐ{an}ÖУ¬¹«±Èq=2, S4=1,ÔòS8=___________.
¡¾±äʽ2¡¿ÒÑÖªµÈ±ÈÊýÁÐ{an}µÄǰnÏîºÍΪSn, ÇÒS10=10, S20=40,Çó£ºS30=£¿ ¡¾±äʽ3¡¿µÈ±ÈÊýÁÐ{an}µÄÏî¶¼ÊÇÕýÊý£¬ÈôSn=80, S2n=6560£¬Ç°nÏîÖÐ×î´óµÄÒ»ÏîΪ54£¬Çón.
SS801¡¾´ð°¸¡¿¡ß n?£¬¡àq?1(·ñÔòn?)
S2n6560S2n2a1(1?qn)¡àSn?=80 ........(1)
1?qa1(1?q2n)S2n?=6560.........(2)£¬
1?q(2)¡Â(1)µÃ£º1+qn=82,¡àqn=81......(3) ¡ß¸ÃÊýÁи÷ÏîΪÕýÊý£¬¡àÓÉ(3)Öªq>1 ¡à{an}ΪµÝÔöÊýÁУ¬¡àanΪ×î´óÏî54. ¡àan=a1qn-1=54,¡àa1qn=54q, ¡à81a1=54q..........(4)
5422¡àa1?q?q´úÈë(1)µÃq(1?81)?80(1?q)£¬
8133¡àq=3,¡àn=4.
¡¾±äʽ4¡¿µÈ±ÈÊýÁÐ{an}ÖУ¬Èôa1+a2=324, a3+a4=36, Ôòa5+a6=_____________. ¡¾±äʽ5¡¿µÈ±ÈÊýÁÐ{an}ÖУ¬Èôa1+a2+a3=7,a4+a5+a6=56, Çóa7+a8+a9µÄÖµ¡£ ÀàÐÍÎ壺µÈ²îµÈ±ÈÊýÁеÄ×ÛºÏÓ¦ÓÃ
Àý5£®ÒÑÖªÈý¸öÊý³ÉµÈ±ÈÊýÁУ¬ÈôǰÁ½Ïî²»±ä£¬µÚÈýÏî¼õÈ¥32£¬Ôò³ÉµÈ²îÊýÁÐ.ÈôÔÙ½«´ËµÈ²îÊýÁеĵڶþÏî¼õÈ¥4£¬ÔòÓֳɵȱÈÊýÁÐ.ÇóÔÀ´µÄÈý¸öÊý.
˼·µã²¦£ºÇ¡µ±µØÉèÔªÊÇ˳Àû½â·½³Ì×éµÄǰÌá.¿¼Âǵ½ÓÐÈý¸öÊý£¬Ó¦¾¡Á¿Éè½ÏÉÙµÄδ֪Êý£¬²¢½«ÆäÉèΪÕûʽÐÎʽ.
×ܽáÉý»ª£ºÑ¡ÔñÊʵ±µÄÉè·¨¿Éʹ·½³Ì¼òµ¥Ò׽⡣һ°ãµØ£¬ÈýÊý³ÉµÈ²îÊýÁУ¬
x¿ÉÉè´ËÈýÊýΪa-d, a, a+d£»ÈôÈýÊý³ÉµÈ±ÈÊýÁУ¬¿ÉÉè´ËÈýÊýΪ£¬x, xy¡£µ«
y»¹Òª¾ÍÎÊÌâ¶øÑÔ£¬ÕâÀï½â·¨¶þÖвÉÓÃÊ×Ïîa£¬¹«±ÈqÀ´½â¾öÎÊÌâ·´¶ø¼ò±ã¡£
¾ÙÒ»·´Èý£º
¡¾±äʽ1¡¿Ò»¸öµÈ±ÈÊýÁÐÓÐÈýÏÈç¹û°ÑµÚ¶þÏî¼ÓÉÏ4£¬£¬ÄÇôËùµÃµÄÈýÏî¾Í
³ÉΪµÈ²îÊýÁУ¬Èç¹ûÔÙ°ÑÕâ¸öµÈ²îÊýÁеĵÚÈýÏî¼ÓÉÏ32£¬ÄÇôËùµÃµÄÈýÏîÓÖ³ÉΪµÈ±ÈÊýÁУ¬ÇóÔÀ´µÄµÈ±ÈÊýÁÐ.
¡¾±äʽ2¡¿ÒÑÖªÈý¸öÊý³ÉµÈ±ÈÊýÁУ¬ËüÃǵĻýΪ27£¬ËüÃÇµÄÆ½·½ºÍΪ91£¬ÇóÕâÈý¸öÊý¡£
¡¾±äʽ3¡¿ÓÐËĸöÊý£¬ÆäÖÐǰÈý¸öÊý³ÉµÈ²îÊýÁУ¬ºóÈý¸öÊý³ÉµÈ±ÈÊýÁУ¬²¢ÇÒµÚÒ»¸öÊýÓëµÚËĸöÊýµÄºÍÊÇ16£¬µÚ¶þ¸öÊýÓëµÚÈý¸öÊýµÄºÍΪ12£¬ÇóÕâËĸöÊý.
ÀàÐÍÁù£ºµÈ±ÈÊýÁеÄÅжÏÓëÖ¤Ã÷
Àý6£®ÒÑÖªÊýÁÐ{an}µÄǰnÏîºÍSnÂú×㣺log5(Sn+1)=n(n¡ÊN+),Çó³öÊýÁÐ{an}µÄͨÏʽ£¬²¢ÅжÏ{an}ÊǺÎÖÖÊýÁУ¿
˼·µã²¦£ºÓÉÊýÁÐ{an}µÄǰnÏîºÍSn¿ÉÇóÊýÁеÄͨÏʽ£¬Í¨¹ýͨÏʽÅжÏ{an}ÀàÐÍ.
¡¾±äʽ2¡¿Éè{an}¡¢{bn}Êǹ«±È²»ÏàµÈµÄÁ½¸öµÈ±ÈÊýÁУ¬Cn=an+bn,Ö¤Ã÷ÊýÁÐ{Cn}²»ÊǵȱÈÊýÁÐ.
¡¾Ö¤Ã÷¡¿ÉèÊýÁÐ{an}¡¢{bn}µÄ¹«±È·Ö±ðΪp, q£¬ÇÒp¡Ùq
2Ϊ֤{Cn}²»ÊǵȱÈÊýÁУ¬Ö»ÐèÖ¤C1?C3?C2. 2?(a1p?b1q)2?a12p2?b12q2?2a1b1pq, ¡ßC2C1?C3?(a1?b1)(a1p2?b1q2)?a12p2?b12q2?a1b1(p2?q2)
2?a1b1(p?q)2, ¡àC1?C3?C2ÓÖ¡ß p¡Ùq, a1¡Ù0, b1¡Ù0,
22?0¼´C1?C3?C2¡àC1?C3?C2
¡àÊýÁÐ{Cn}²»ÊǵȱÈÊýÁÐ.
¡¾±äʽ3¡¿ÅжÏÕýÎó£º
(1){an}ΪµÈ±ÈÊýÁÐ?a7=a3a4£»
(2)Èôb2=ac£¬Ôòa£¬b£¬cΪµÈ±ÈÊýÁУ»
(3){an}£¬{bn}¾ùΪµÈ±ÈÊýÁУ¬Ôò{anbn}ΪµÈ±ÈÊýÁУ»
?1?2{a}(4){an}Êǹ«±ÈΪqµÄµÈ±ÈÊýÁУ¬Ôòn¡¢??ÈÔΪµÈ±ÈÊýÁУ»
?an?(5)Èôa£¬b£¬c³ÉµÈ±È£¬Ôòlogma£¬logmb£¬logmc³ÉµÈ²î. ÀàÐÍÆß£ºSnÓëanµÄ¹ØÏµ
2?5an?6£¬ÇÒa1£¬a3£¬Àý7£®ÒÑÖªÕýÏîÊýÁÐ{an}£¬ÆäǰnÏîºÍSnÂú×ã10Sn?ana15³ÉµÈ±ÈÊýÁУ¬ÇóÊýÁÐ{an}µÄͨÏîan.
¾ÙÒ»·´Èý£º
¡¾±äʽ¡¿ÃüÌâ1£ºÈôÊýÁÐ{an}µÄǰnÏîºÍSn=an+b(a¡Ù1)£¬ÔòÊýÁÐ{an}ÊǵȱÈÊýÁУ»ÃüÌâ2£ºÈôÊýÁÐ{an}µÄǰnÏîºÍSn=na-n£¬ÔòÊýÁÐ{an}¼ÈÊǵȲîÊýÁУ¬ÓÖÊǵȱÈÊýÁС£ÉÏÊöÁ½¸öÃüÌâÖУ¬ÕæÃüÌâΪ ¸ö.
Ïà¹ØÍÆ¼ö£º