已知数列an满足an=31-6n,数列bn满足bn=(a1+a2+...+an)/n,求数列/bn/的前20项之和A.187 B.164 C.257 D.304
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![已知数列an满足an=31-6n,数列bn满足bn=(a1+a2+...+an)/n,求数列/bn/的前20项之和A.187 B.164 C.257 D.304](/uploads/image/z/13731806-38-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97an%E6%BB%A1%E8%B6%B3an%3D31-6n%2C%E6%95%B0%E5%88%97bn%E6%BB%A1%E8%B6%B3bn%3D%28a1%2Ba2%2B...%2Ban%29%2Fn%2C%E6%B1%82%E6%95%B0%E5%88%97%2Fbn%2F%E7%9A%84%E5%89%8D20%E9%A1%B9%E4%B9%8B%E5%92%8CA.187+B.164+C.257+D.304)
已知数列an满足an=31-6n,数列bn满足bn=(a1+a2+...+an)/n,求数列/bn/的前20项之和A.187 B.164 C.257 D.304
已知数列an满足an=31-6n,数列bn满足bn=(a1+a2+...+an)/n,求数列/bn/的前20项之和
A.187 B.164 C.257 D.304
已知数列an满足an=31-6n,数列bn满足bn=(a1+a2+...+an)/n,求数列/bn/的前20项之和A.187 B.164 C.257 D.304
a1=31-6=25
a1+a2+...+an = (a1+an)n/2 =(28-3n)n
bn=(a1+a2+...+an)/n = 28-3n >0
n < 28/3
说 b9>0,b10
a1=31-6*1=25
a(n+1)-an=31-6*(n+1)-(31-6n)=-6
Sn=a1+a2+....+an=n*a1+(-6)*[1+2+.....+(n-1)]=25n-3n(n-1)=28n-3n^2
bn=(28n-3n^2)/n=28-3n
b1=28-3*1=25
b(n+1)-bn=28-3(n+1)-(28-3n)=-3
S20=b1+b2+.....+b20=20*b1-3*(1+2+...+19)=20*25-3*(1+19)*19/2=-70