已知a1a2a3a4成等比数列,且a1＝a2＋36,a3＝a4＋4,求a1a2a3a4

来源：学生作业帮助网编辑：作业帮时间：2024/05/07 11:30:03

已知a1a2a3a4成等比数列,且a1＝a2＋36,a3＝a4＋4,求a1a2a3a4
已知a1a2a3a4成等比数列,且a1＝a2＋36,a3＝a4＋4,求a1a2a3a4

已知a1a2a3a4成等比数列,且a1＝a2＋36,a3＝a4＋4,求a1a2a3a4
刷粉

等比数列性质：a1/a2=a2/a3=a3/a4,a1/a3=a2/a4,
两式相除：a1/a3=（a2＋36）/（a4＋4）=a2/a4.交叉相乘解得：a2/a4=9
得：a1/a2=a2/a3=a3/a4=3。代入a1＝a2＋36，a3＝a4＋4可得：a1＝54，a2=18，a3＝6，a4=2

设a2=xa1,a3=x2a1,a4=x3a1,代入等式：a1=xa1+36; x2a1=x3a1+4;处理后：a1=36/(1-x);xa1=4/(x-x2);代入a1：36x/(1-x)=4/x(1-x);化简：x2=1/9; x=1/3或x=-1/3; 结果：a1=54,a2=18,a3=6,a4=2;或a1=27,a2=-9;a3=3,a4=-1;

已知a1a2a3a4成等比数列,且a1＝a2＋36,a3＝a4＋4,求a1a2a3a4 已知等差数列(an)满足a1=2,且a1,a2,a5成等比数列已知A1 A2 A3 A4 成等比数列且A1＝A2＋36 A3＝A4＋4 求A1 A2 A3 A4 已知等差数列｛An｝的公差不为零,a1＝25,且a1,a11,a13成等比数列.求a1+a4+a7+.a3n-2 已知数列{a}是公差不为零的等差数列,若a1=1,且a1a2a3成等比数列an=且a1，a2，a3成等比数列an= 在公差为d的等差数列{an}中已知a1＝10,且a1.2a2+2.5a3成等比数列,求d和an 已知｛an｝是公差不为0的等差数列,a1＝1且a1,a3,a9成等比数列.求数列｛an｝的通项公式已知数列｛an｝是等比数列,且a4＝－27,a1＝1求a5,a8 已知等差数列{an}的公差d不等于0且a1,a3,a9成等比数列,则看图已知数列an是等比数列,且a1,a2,a4成等差数列,求数列an的公比已知An是等比数列,且a1,a2,a4成等差数列,求数列{an}公比已知等比数列｛an｝,且a1,a2,a4成等差数列,求｛an｝的公比已知等比数列{An},a1=3,且4a1 2a2 a3成等差数列,则a3+a4+a5等于? 已知等比数列{An},a1=3,且4a1 2a2 a3成等差数列,则a3+a4+a5等于? 已知｛an｝是公差不为0的等差数列,a1=1,且a1,a3,a9成等比数列.求通项公式已知an是等比数列,如果lim（a1+a2+```+an）=2,且a3,a5,a6成等差数列,则a1 已知{an}的公差不为零的等差数列,a1＝1,且a1 a3 a9成等比数列.①求{an...已知{an}的公差不为零的等差数列,a1＝1,且a1 a3 a9成等比数列.①求{an}的通项. ②记bn＝(n+1)2∧an,求数列{bn}的前n项和Sn .要已知公差不为零的等差数列{an}中,a1＝1,且a1,a3,a13成等比数列． (1)求数列{an}的通项公式； (2)设bn已知公差不为零的等差数列{an}中,a1＝1,且a1,a3,a13成等比数列．(1)求数列{an}的通项公式；(2)设bn