中四數學題....數列

5, 27, 49,

This is Arithmetic sequence
The common difference, d = (27 – 5) = 22, (49 -27) = 22
The first term, a = 5

The general term tn = a + (n-1)d
Foe 72th term, n = 72
t72 = 5 +(72 -1)22 = 5 + 71(22) = 5 + 1562 = 1567

72項是1567

Arithmetic series

Sn = n/2[2a + (n-1)d]
S72 = 72/2[2(5) + (72-1)22]
S72 = 36[10 + (71)22]
S72 = 36[10 + 1562]
S72 = 36[1572]
S72 = 56592

第1項到第72項的總和是56592

2011-01-13 10:37:17 補充：
Arithmetic sequence = 等差序列
Common difference, d = 公差 , 公差是 22
first item, a = 首項, 首項是 5

General term = 通項 ,
通項是tn = a + (n-1)d

Arithmetic Series = 等差级数,
等差级数是Sn = n/2 [2a + (n-1)d]

2011-01-13 11:01:09 補充：
除了這個公式, Sn = n/2[2a + (n-1)d]

另外一個公式,第1項到第n項的總和, Sn =n/2 (t1 + tn)

第1項到第72項的總和, S72 =72/2 (5 + 1567) = 56592