Question

问两道数列题设Sn是等差数列{an}的前n项和,已知S6=36,Sn=324,S(n-6)=144,则n=?A15 B1

Answer 1

1.

选D

Sn是等差数列

S6=a1*6+6(6-1)/2*d=36,则2a1+5d=12 ①

最后六项的和S=an*6-6(6-1)/2*d=6an-15d

S(n-6)=Sn-S=324-(6an-15d)=144,则2an-5d=60 ②

①+②:a1+an=36

Sn=(a1+an)/2*n

n=18

2.

选B

S4=1

S8=3

S8-S4=2

q^4=(S8-S4)/S4=2

补充：S8-S4=a5+a6+a7+a8=q^4*(a1+a2+a3+a4)

a17+a18+a19+a20

=(a1+a2+a3+a4)*q^16

=S4*q^16

=1*2^4

=16

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