设等比数列{an}的前n项和sn,sn=3的n次方+a,则a=?由等比数列求和公式s(n)=a(1)(q^n-1)/(q-1)得a(1)(q^n-1)/(q-1)=3^n+a化简得a(1)q^n-a(1)=(q-1)3^n+a(q-1)【【【【左右两边对应可得q=3 a(1)=q-1=2 a(q-1)=-a(1)2a=-2即a=-
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 18:47:25
![设等比数列{an}的前n项和sn,sn=3的n次方+a,则a=?由等比数列求和公式s(n)=a(1)(q^n-1)/(q-1)得a(1)(q^n-1)/(q-1)=3^n+a化简得a(1)q^n-a(1)=(q-1)3^n+a(q-1)【【【【左右两边对应可得q=3 a(1)=q-1=2 a(q-1)=-a(1)2a=-2即a=-](/uploads/image/z/7231316-68-6.jpg?t=%E8%AE%BE%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8Csn%2Csn%3D3%E7%9A%84n%E6%AC%A1%E6%96%B9%2Ba%2C%E5%88%99a%3D%3F%E7%94%B1%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%E6%B1%82%E5%92%8C%E5%85%AC%E5%BC%8Fs%28n%29%3Da%281%29%28q%5En-1%29%2F%28q-1%29%E5%BE%97a%281%29%28q%5En-1%29%2F%28q-1%29%3D3%5En%2Ba%E5%8C%96%E7%AE%80%E5%BE%97a%281%29q%5En-a%281%29%3D%28q-1%293%5En%2Ba%28q-1%29%E3%80%90%E3%80%90%E3%80%90%E3%80%90%E5%B7%A6%E5%8F%B3%E4%B8%A4%E8%BE%B9%E5%AF%B9%E5%BA%94%E5%8F%AF%E5%BE%97q%3D3++++a%281%29%3Dq-1%3D2++++a%28q-1%29%3D-a%281%292a%3D-2%E5%8D%B3a%3D-)
设等比数列{an}的前n项和sn,sn=3的n次方+a,则a=?由等比数列求和公式s(n)=a(1)(q^n-1)/(q-1)得a(1)(q^n-1)/(q-1)=3^n+a化简得a(1)q^n-a(1)=(q-1)3^n+a(q-1)【【【【左右两边对应可得q=3 a(1)=q-1=2 a(q-1)=-a(1)2a=-2即a=-
设等比数列{an}的前n项和sn,sn=3的n次方+a,则a=?
由等比数列求和公式
s(n)=a(1)(q^n-1)/(q-1)
得a(1)(q^n-1)/(q-1)=3^n+a
化简得
a(1)q^n-a(1)=(q-1)3^n+a(q-1)
【【【【左右两边对应可得
q=3 a(1)=q-1=2 a(q-1)=-a(1)
2a=-2即a=-1】】】←这里不懂能解释下么.谢谢!
设等比数列{an}的前n项和sn,sn=3的n次方+a,则a=?由等比数列求和公式s(n)=a(1)(q^n-1)/(q-1)得a(1)(q^n-1)/(q-1)=3^n+a化简得a(1)q^n-a(1)=(q-1)3^n+a(q-1)【【【【左右两边对应可得q=3 a(1)=q-1=2 a(q-1)=-a(1)2a=-2即a=-
这是个恒等式,n取值为任何非负整数均成立,因此就要求有n的项目对应的系数等均要相同.这里等号右侧有一个3^n,因此左侧也要有一个3^n,且3^n前面的系数要相等.
因此左侧的q^n=3^n,即q=3.
a(1)*3^n=(3-1)*3^n,因此a(1)=2.
-a(1)=a*(q-1)=2*a,因此-2=2*a,a=-1.
a(1)q^n-a(1)=(q-1)3^n+a(q-1)
左右两边对应可得
a(1)q^n=(q-1)3^n,-a(1)=a(q-1)
∴a(1)=q-1,q=3,a(q-1)=-a(1),
将q=3代入a(1)=q-1,得a(1)=2,
将q=3,a(1)=2代入a(q-1)=-a(1),得(3-1)a=-2,∴a=-1。