SPOILER
設各邊邊長為a1,a2,...an, a1<a2<...<an
=>
1)a1 = an - 3(n-1)
2)7a1=an
(2) -> (1): a1=7a1 - 3(n-1)
n=2a1+1
trial:
a1=1, n=3, an=7, sum = 12
a1=2, n=5, an=14, sum = 40
a1=3, n=7, an=21, sum = 84
a1=4, n=9, an=28, sum = 144
a1=5, n=11, an=35, sum = 220
a1=6, n=13, an=42, sum = 312 <- 正解
check: when n increase, sum monotonically increase
OR
sum = (a1+an)n/2 = (a1+7a1)(2a1+1)/2=8a1^2+4a1=312
4(2a1+13)(a1-6)=0
a1=-13/2 (reject) or a1=6
=> n=13 是唯一解。
=>
1)a1 = an - 3(n-1)
2)7a1=an
(2) -> (1): a1=7a1 - 3(n-1)
n=2a1+1
trial:
a1=1, n=3, an=7, sum = 12
a1=2, n=5, an=14, sum = 40
a1=3, n=7, an=21, sum = 84
a1=4, n=9, an=28, sum = 144
a1=5, n=11, an=35, sum = 220
a1=6, n=13, an=42, sum = 312 <- 正解
check: when n increase, sum monotonically increase
OR
sum = (a1+an)n/2 = (a1+7a1)(2a1+1)/2=8a1^2+4a1=312
4(2a1+13)(a1-6)=0
a1=-13/2 (reject) or a1=6
=> n=13 是唯一解。
呃 又離題了
你啥时候能把我的名字改对了。。。