已知数列的前n项和为Sn=an²+bn(a,b属于R)且S25=100,则a12=a11为?
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![已知数列的前n项和为Sn=an²+bn(a,b属于R)且S25=100,则a12=a11为?](/uploads/image/z/5541645-21-5.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%3Dan%26%23178%3B%2Bbn%EF%BC%88a%2Cb%E5%B1%9E%E4%BA%8ER%EF%BC%89%E4%B8%94S25%3D100%2C%E5%88%99a12%3Da11%E4%B8%BA%3F)
已知数列的前n项和为Sn=an²+bn(a,b属于R)且S25=100,则a12=a11为?
已知数列的前n项和为Sn=an²+bn(a,b属于R)且S25=100,则a12=a11为?
已知数列的前n项和为Sn=an²+bn(a,b属于R)且S25=100,则a12=a11为?
an=sn-s(n-1)
=an²+bn-a(n-1)²-b(n-1)
=2an-a+ba(n-1)=2a(n-1)-a+ban-a(n-1)=2an-a+b-2a(n-1)+a-b=2a,为定值.数列{an}是以a+b为首项,2a为公差的等差数列.S25=25(a+b)+25×24×2a/2=625a+25b=10025a+b=4