16.已知一等比級數公比為3，末項為486，又級數和為728

12.等比數列a8=20，a15=-5/32，則其公比為(A)1/2(B)-1/2(C)3/2(D)-3/2a8=a*r^7=20a15=a*r14=-5/32相除: r^7=-1/2^7 => r=-1/2.....ans=(B)


2014-03-16 19:39:07 補充：
13.等比數列a3=10，a6=-5/4，則a10=?(A)5/64(B)-5/64(C)-5/128(D)5/128

a3=a*r^2=10

a6=a*r^5=-5/4

相除:r^3=-1/2^3 => r=-1/2

a=10/r^2=40

a10=40*r^9

=-40/2^9

=-5/64.....ans=(B)

2014-03-16 19:47:46 補充：
17.等比數列√2-1，1，√2+1，3+2√2，...的第n項為

(A)根號2(2-根號2)^2(B)(根號2+1)^n-1

(C)(根號2+1)^n-2(D)(根號2-1)(2+根號2)^n-1

a=√2-1, r=√2+1

an=a*r^(n-1)

=(√2-1)*(√2+1)^(n-1)

=(√2-1)*(√2+1)*(√2+1)^(n-2)

=(√2+1)^(n-2).....ans=(C)

2014-03-16 19:54:46 補充：
15.等比級數a=25，公比r=-2，S=-8525，則此級數共有(A)9(B)10(C)11(D)12項

S=a(r^n-1)/(r-1)

=> r^n=[S(r-1)/a]+1

=-8525(-3)/25+1

=341*3+1

=1024

=2^10

=> n=10.....ans=(B)

2014-03-16 20:07:31 補充：
16.等比級數r=3，an=486，Sn=728，則其項數n=(A)4(B)5(C)6(D)7

an=a*r^(n-1)

=486

=2*243

=2*3*81

=2*3^5

=> a=2, n=6.....ans(6)

2014-03-16 20:10:59 補充：
18.等比級數1+3+3^2+...+3^n的和為3280，則n=(A)6(B)7(C)8(D)9

Sn=a*(r^n-1)/(r-1)

3280=1*(3^n-1)/2

3^n=6560+1

=6561

=729*9

=81*81

=3^8

=> n=8.....ans=(C)

2014-03-16 20:17:20 補充：
20.無窮等比級數0.36+0.036+0.0036+0.00036+...的和為(A)2/5(B)3/5(C)4/15

(D)7/15

r=0.1, a=0.36

Lim(n->oo)Sn

=0.36*(1-0.1^n)/(1-0.1)

=0.36/0.9

=36/90

=4/10

=2/5.....ans(A)

2014-03-16 20:24:09 補充：
21.無窮等比級數a2=-2，a5=16/27，則此級數和S=?

(A)7/3(B)8/3(C)8/5(D)9/5

a2=a*r=-2

a5=a*r^4=16/27

相除: r^3=-8/27 => r=-2/3

=> a=-2/r=3

S=a*(1-r^n)/(1-r)

=3*[1-(-2/3)^n]/(5/3)

=3*1/(5/3)

=9/5.....ans=(D)

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http://phi008780520.pixnet.net/blog