數列:1,4,8,12... 求第5個數

第5個數是16
單數:1,3,5,7,9
第1個數:1=1
第2個數:1+3=4
第3個數:3+5=8
第4個數:5+7=12
第5個數:7+9=16
So,第5個數=16
第6個數:20
數列:1,4,812,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80, ...



2009-06-18 14:01:03 補充：
數列:1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80, ...

Let An=an^3+bn^2+cn+d
A1 = a + b + c + d = 1 ...(1)
A2 = 8a + 4b + 2c + d = 4 ...(2)
A3 = 27a + 9b + 3c + d = 8 ... (3)
A4 = 64a + 16b + 4c + d= 12 ... (4)

(1)-(2)=>
7a + 3b + c = 3 ... (5)
(3)-(2)=>
19a + 5b + c = 4 ... (6)
(4)-(3)=>
37a + 7b + c = 4 ... (7)

(6)-(5) =>
12a + 2b = 1 ... (8)
(7)-(6) =>
18a + 2b = 0 ... (9)

(9)-(8) =>
6a = -1
a = -1/6

Sub into (9),
-3+2b =0
b= 3/2

Sub into (7),
-7/6 + 9/2 + c = 3
c=-1/3

Sub into (1),
-1/6 + 3/2 - 1/3 + d = 1
d=0

So An=-1/6n^3+3/2n^2-n/3
An = -n(n^2-9n+2)/6

A5 = (-5)(25-45+2)/6 = (-5)(-18)/6 = 15

1, 4, 8, 12 ....

T(1) = 1 = 4 x 0 = 4 x (1 - 1)
T(2) = 4 = 4 x 1 = 4 x (2 - 1)
T(3) = 8 = 4 x 2 = 4 x (3 - 1)
T(4) = 12 = 4 x 3 = 4 x (4 - 1)

所以通用公式為 T(n) = 4 x (n - 1)
n 為第 n 項的代數

現在我們要計第 5 項
所以代 n = 5

T(5) = 4 x (5 - 1) = 4 x 4 = 16