已知等差数列{an}的前n项和为Sn,且满足a2+a4=14,S7=70
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已知等差数列{an}的前n项和为Sn,且满足a2+a4=14,S7=70
设bn=(2Sn+48)/n,求数列bn的最小项是第几项?并求出该项的值
设bn=(2Sn+48)/n,求数列bn的最小项是第几项?并求出该项的值
![已知等差数列{an}的前n项和为Sn,且满足a2+a4=14,S7=70](/uploads/image/z/6570439-7-9.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E4%B8%94%E6%BB%A1%E8%B6%B3a2%2Ba4%3D14%2CS7%3D70)
an=a1+(n-1)d
a2+a4=14
2a1+4d =14
a1+2d =7 (1)
S7=70
(a1+3d)7 =70
a1+3d =10 (2)
(2)-(1)
d=3
a1=1
an = 1+(n-1)3 = 3n-2
bn = (2Sn+48)/n
= [(3n-1)n+48]/n
= (3n^2-n+48)/n
let
f(x) = (3x^2-x+48)/x
f'(x) = 3- 48/x^2 =0
3x^2-48=0
x= 4
f''(x) = 96/x^3
f''(4)>0 (min)
min bn at n=4
min bn = b4
= (48-4+48)/4
= 92/4
=23
a2+a4=14
2a1+4d =14
a1+2d =7 (1)
S7=70
(a1+3d)7 =70
a1+3d =10 (2)
(2)-(1)
d=3
a1=1
an = 1+(n-1)3 = 3n-2
bn = (2Sn+48)/n
= [(3n-1)n+48]/n
= (3n^2-n+48)/n
let
f(x) = (3x^2-x+48)/x
f'(x) = 3- 48/x^2 =0
3x^2-48=0
x= 4
f''(x) = 96/x^3
f''(4)>0 (min)
min bn at n=4
min bn = b4
= (48-4+48)/4
= 92/4
=23
已知等差数列{an}的前n项和为Sn,且满足:a2+a4=14,S7=70.
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