设Sn是等差数列{an}的前n项和,已知S6=36,Sn=324,Sn-6=144（n>6),则n等于?

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设Sn是等差数列{an}的前n项和,已知S6=36,Sn=324,Sn-6=144（n>6),则n等于?
设Sn是等差数列{an}的前n项和,已知S6=36,Sn=324,Sn-6=144（n>6),则n等于?

设Sn是等差数列{an}的前n项和,已知S6=36,Sn=324,Sn-6=144（n>6),则n等于?
Sn - S = 324 - 144
a + a + a + a + a + a = 180
a1 + a2 + a3 + a4 + a5 + a6 = 36
两式子相减
(a - a1) + (a - a2) + …… + (a - a6) = 180 - 36
(n-6)d + (n-6)d + (n-6)d + (n-6)d + (n-6)d + (n-6)d = 144
6(n-6)d = 144
(n-6)d = 24
S6 = 36
(2a1 + 5d)*6/2 = 36
2a1 = 12 - 5d
Sn = 324
[2a1 + (n-1)d] *n /2 =324
(12 - 6d + nd) * n = 648
[12 + (n-6)d] * n = 648
(12 + 24)*n = 648
n = 648/36 = 18

n=18,an=1,3,5,7,...,35.

n = 648/36 = 18

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