描述下列數的規律

回答如下 : -

1) 1 , 4 , 8 , 13 , 19 , 26
1(+3) = 4
4(+4) = 8
8(+5) = 13
13(+6) = 19
19(+7) = 26
** 加數數字遞增+1

2) 1 , 1 , 0 , 1, -1 , 2
1-1 = 0
1-0 = 1
0-1 = -1
1-(-1) = 2
** 前2數相加等於第3個數

a) T1 = 1 = 1+ 2 - 2 = 2 * 3 / 2 - 2
T2 = 4 = 1 + 2 + 3 - 2 = 3 * 4 / 2 - 2
T3 = 8 = 1 + 2 + 3 + 4 - 2 = 4 * 5 / 2 - 2
T4 = 13 = 1 + 2 + 3 + 4 + 5 - 2 = 5 * 6 / 2 - 2
T5 = 19 = 1 + 2 + 3 + 4 + 5 + 6 - 2 = 6 * 7 / 2 - 2
T6 = 26 = 1 + 2 + 3 + 4 + 5 + 6 + 7 - 2 = 7 * 8 / 2 - 2
therefore Tn = (n + 1)*(n + 2) / 2 - 2. OR the term is the sum of the first (n+1) numbers minus 2.

b) T1 = 1
T2 = 1
T3 = 0 = 1 - 1 = T1 - T2
T4 = 1 = 1 - 0 = T2 - T3
T5 = -1 = 0 - 1 = T3 - T4
T6 = 2 = 1 - (-1) = T4 - T5
therefore, except T1=T2=1, Tn = T(n-2) - T(n-1) for n greater than or equal to 2.
OR except T1=T2=1, for terms greater than or equal to 2, it is the previous second term minus the previous term.