根据下列条件,求相应的等差数列{an}的有关未知数:(1) a1=20,an=54,Sn=999,求d和n(2) d=1/3,n=37,Sn=629,求a1和an(3) a1=5/6,d=-1/6,Sn=-5,求n和an(4) d=2,n=15,an=-10,求a1和Sn
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根据下列条件,求相应的等差数列{an}的有关未知数:(1) a1=20,an=54,Sn=999,求d和n(2) d=1/3,n=37,Sn=629,求a1和an(3) a1=5/6,d=-1/6,Sn=-5,求n和an(4) d=2,n=15,an=-10,求a1和Sn
根据下列条件,求相应的等差数列{an}的有关未知数:
(1) a1=20,an=54,Sn=999,求d和n
(2) d=1/3,n=37,Sn=629,求a1和an
(3) a1=5/6,d=-1/6,Sn=-5,求n和an
(4) d=2,n=15,an=-10,求a1和Sn
根据下列条件,求相应的等差数列{an}的有关未知数:(1) a1=20,an=54,Sn=999,求d和n(2) d=1/3,n=37,Sn=629,求a1和an(3) a1=5/6,d=-1/6,Sn=-5,求n和an(4) d=2,n=15,an=-10,求a1和Sn
1.
Sn=(a1+an)n/2
n=2Sn/(a1+an)=2×999/(20+54)=27
an=a1+(n-1)d
d=(an-a1)/(n-1)=(54-20)/(27-1)=1
d=1 n=27
2.
Sn=na1+n(n-1)d/2
a1=[Sn-n(n-1)d/2]/n=[629-37×(37-1)×(1/3)/2]/37=11
an=a1+(n-1)d=11+(37-1)×(1/3)=23
a1=11 an=23
3.
Sn=na1+n(n-1)d/2
-5=(5/6)n+n(n-1)(-1/6)/2
整理,得
n²-11n-60=0
(n-15)(n+4)=0
n=15或n=-4(n>0,舍去)
an=a1+(n-1)d=5/6 +(15-1)(-1/6)=-3/2
n=15 an=-3/2
4.
an=a1+(n-1)d
a1=an-(n-1)d=-10-(15-1)×2=-38
Sn=(a1+an)n/2=(-38-10)×15/2=-360
a1=-38 Sn=-360
(1)n=27,d=17/13
(2)a1=11,an=23
(3)n=15,an=-5/3
(4)a1=-38,sn=-360
分析,
1,Sn=n(a1+an)/2
∴n=27
d=(a27-a1)/26
=17/13
2,Sn=a1*n+n(n-1)d/2
∴a1=11
a37=a1+36d
=23
3,Sn=a1*n+n(n-1)d/2
-5=5n/6+n(n-1)*(-1/6)*(1/2)
解出,n=-4...
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分析,
1,Sn=n(a1+an)/2
∴n=27
d=(a27-a1)/26
=17/13
2,Sn=a1*n+n(n-1)d/2
∴a1=11
a37=a1+36d
=23
3,Sn=a1*n+n(n-1)d/2
-5=5n/6+n(n-1)*(-1/6)*(1/2)
解出,n=-4(舍去)或n=15
a15=a1+14d
=-3/2
4,an=a1+(n-1)d
a1=-38
Sn=n(a1+an)/2
∴Sn=-360。
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(1) a1=20,an=54,Sn=999,求d和n
Sn=(a1+an)n/2 999=37n n=27
an=a1+(n-1)d 54=20+26d d=17/13
(2) d=1/3,n=37,Sn=629,求a1和an
Sn=na1+n(n-1)d/2 629=37a1+37*6...
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(1) a1=20,an=54,Sn=999,求d和n
Sn=(a1+an)n/2 999=37n n=27
an=a1+(n-1)d 54=20+26d d=17/13
(2) d=1/3,n=37,Sn=629,求a1和an
Sn=na1+n(n-1)d/2 629=37a1+37*6 17=a1+6 a1=11
an=a1+(n-1)d=11+36*1/3=23
(3) a1=5/6,d=-1/6,Sn=-5,求n和an
Sn=na1+n(n-1)d/2 -5=5n/6+n(n-1)*(-1/6)/2 n^2-n-10n=60
n^2-11n-60=0 n=-4(舍)或n=15
an=a1+14d=5/6-14/6=-3/2
(4) d=2,n=15,an=-10,求a1和Sn
an=a1+(n-1)d -10=a1+14*2 a1=-38
Sn=(a1+an)n/2=-48*15/2=--360
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