已知等比数列{an}，a1=3，公比q=2，求a5 已知等比数列{An}的首项A1=3,公比q=2,则S5等于多...
\u5df2\u77e5\u7b49\u6bd4\u6570\u5217{an}\u4e2d\uff0ca1=3,q=1/2,\u5219a5=a5=a1*q^4
=3*(1/2)^4
=3/16
s5=A1\uff081-qn\uff09/(1-q)=3*\uff081-25\uff09/\uff081-2\uff09=93\u5176\u4e2dqn\u662f\u8868\u793aq\u7684n\u6b21\u65b9\u6ee1\u610f\u5417
a5＝a1×q＾4＝3×16＝48绛旓細鍥犱负绛夋瘮鏁板垪{an}鐨勯氶」鍏紡涓猴細an = a1 * r^(n-1)浠ｅ叆宸茬煡鏉′欢锛屾湁锛歛n = 3 * 2^(n-1)鍥犳锛岀瓑姣旀暟鍒楃殑閫氶」鍏紡鏄痑n=3*2^(n-1)銆傜壒鍒湴锛宎3鏄瘂an}鐨勭3椤癸紝灏唍=3浠ｅ叆绛夋瘮鏁板垪鐨勯氶」鍏紡锛屽彲寰楋細a3 = 3 * 2^(3-1) = 12 鍥犳锛岀瓑姣旀暟鍒楃殑绗笁椤逛负a3=12銆
绛旓細鏍规嵁an=a1q^(n-1)a5=a1脳q^4 浠ｄ汉 48=3脳q^4 q^4=16 q=2鎴-2 鏍规嵁sn=a1锛1-q^n锛/(1-q)q=2鏃跺 sn=3(2^n-1)q=-2鏃跺 sn=1-(-2)^n
绛旓細an=a1*q^(n-1)鈭 3/64=3*(1/2)^(n-1)鈭 1/64=(1/2)^(n-1)鈭 n-1=6 鈭 n=7
绛旓細瑙ｏ細鍥犱负a(n+1)=2an+3鏁咃細a(n+1)+3=2锛坅n+3锛夋晠锛沎a(n+1)+3]/ 锛坅n+3锛=2鏁咃細(a2+3)/(a1+3)=2(a3+3)/(a2+3)=2(a4+3)/(a3+3)=2鈥︹︼紙an+3锛/[a(n-1)+3]=2宸﹀彸涓よ竟鐩镐箻锛氾紙an+3锛/(a1+3)=2^(n-1)鍥犱负a1=3鏁咃細an+3=3脳2^n鏁咃細an=3脳2^n-3 ...
绛旓細+p/2 瑕乹涓烘鏁存暟,鍙p涓烘鍋舵暟.b2=2脳2+1=5 b(2n)-b(2n-2)=2*(2n)+1-[2*(2n-2)+1]=4,涓哄畾鍊 鏁板垪{b(2n)}鏄互5涓洪椤,4涓哄叕宸殑绛夊樊鏁板垪,鏁板垪鍗曡皟閫掑,鍙栧嚭鏁板垪{an}鐨勫鏁伴」,鎸夊師椤哄簭鎺掑垪,鍗虫瀯鎴愭暟鍒梴dn} dn=5+4(n-1)=4n+1 S100=(5+401)*100/2=20300 ...
绛旓細鏁板垪{an}婊¤冻a1=3锛7an+1=an锛坣鈭圢*锛夛紝鍒欐鏁板垪鏄椤逛负3锛屽叕姣斾负1/7鐨绛夋瘮鏁板垪锛鎵浠 an=3*(1/7)^(n-1)=3/[7^(n-1)]
绛旓細锛1锛夎В锛氱敱S锛坣+1锛=3Sn+2n寰桽n=3S锛坣-1锛+2n-2锛屼袱寮忕浉鍑忥紝寰梐n+1=3an+2锛屼袱杈瑰悓鏃跺姞1锛屽緱a锛坣+1锛+1=3锛坅n+1锛夛紝鍗砤锛坣锛+1鏄叕姣斾负3鐨勭瓑姣旀暟鍒椼傚洜姝锛坣锛+1=锛a1+1)3^n-1=4*3^锛坣-1锛.,寰梐n=4*3^(n-1锛-1銆傜患涓婏紝a锛坣锛+1鏄叕姣斾负3鐨绛夋瘮鏁板垪锛宎n閫...
绛旓細s5=A1锛1-qn锛/(1-q)=3*锛1-25锛/锛1-2锛=93鍏朵腑qn鏄〃绀簈鐨刵娆℃柟婊℃剰鍚
绛旓細an=a1脳q^(n-1)an=3脳2^(n-1)鈥︽墍浠4=3脳2^3=24
绛旓細鈭a1=3,an+1+an=3*2^n,n鈭圢*)鈭碼(n+1)=3*2^n-an 鈭碵a(n+1)-2^(n+1)]/(an-2^n)=[3*2^n-an-2*2^n]/(an-2^n)=(2^n-an)/(an-2^n)=-1锛堝父鏁板畾鍊硷級鈭鏁板垪{an-2^n}鏄绛夋瘮鏁板垪銆傘愬叕姣斾负-1銆
