Question

设Sn为等差数列{an}的前n项和,己知S6=36,Sn=324,S(n-6)=144,(n>6)则n=多少?

Answer 1

Sn是等差数列
S6=a1*6+6(6-1)/2*d=36，则2a1+5d=12……a
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……b
由上述a+b得：a1+an=36
Sn=(a1+an)/2*n =324
n=18

Answer 2

Sn是等差数列
S6=a1*6+6(6-1)/2*d=36，则2a1+5d=12......&
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......@
&+@:a1+an=36
Sn=(a1+an)/2*n =324
n=18

Answer 3

(a1+a2+a3+a4+a5+a6)+(an+an-1+...+an-5)=36+324-144=216=(a1+an)*6得
a1+an=36
Sn=(a1+an)*n/2
324=18n
n=18