超易S1 Maths 20點 送分

For geometric sequence, 4, 16, 64, 256, ….

The general term is given by tn = ar^(n-1)

Where a is the first term, n is the number of term, r is common ratio

a = 4

r = 16/4 = 4, 64/26 = 4, 256/64 = 4

common ratio r = n term / previous term

tn = 4 x 4^(n-1) (x =乘, ^ raise to the power e.g. 4^3 = 4自乘三次 = 64)

First term (n = 1), t1 = 4 x 4^(1-1) = 4 x 4^(0) = 4 x 1 = 4
Second term (n = 2), t2 = 4 x 4^(2-1) = 4 x 4^(1) = 4 x 4 = 16
Third term (n = 3), t3 = 4 x 4^(3-1) = 4 x 4^(2) = 4 x 16 = 64
Fourth term (n = 4), t4 = 4 x 4^(4-1) = 4 x 4^(3) = 4 x 64 = 56

For term n,
tn = 4 x 4^(n-1)

This only applies to geometric sequence, 4, 16, 64, 256, ….

Another example, for geometric sequence 3, 6, 12, 24 .......
a = 3, r = 6/3 =2, 12/6 =2, 24/12 = 2

For term n,
tn = 3 x 2^(n-1)
 
Comment:
I hope you know the arithmetic sequence as well.



2010-12-15 08:00:14 補充：
Sequence 有不同種類
For Arithmetic Sequence,
Term is given by: tn = a + (n-1)d
Where a = first term, n is number of term, and d = is the common difference.
Common difference = term n – previous term
For example: 2,5,8,11, ….
a = 2, d = 3 (given by 5 -2)
tn = 2 + (n-1)3

問題是決定那一類Sequence.

幫下你啦:
e.g.
The general term of a sequence is 2n-1. Find
(a) The first five terms,
(b)the 10th term

Of the sequence.
General term, An=2n-1
(a)
A1=2*1-1=1
A2=2*2-1=3
A3=2*3-1=5
A4=2*4-1=7
A5=2*5-1=9
The first terms of the sequence are 1, 3, 5, 7 and 9.
(b)A15=2(15)-1=29
The 15th term of the sequence is 29.