AQA_Bk1_chap14_Layout 1 21/01/2010 17:01 Page 436
CHAPTER 14: Algebra: Patterns
C
The formula for working out a series of fractions is
PS
a
2n + 1
.
3n + 1
Work out the first three fractions in the series.
b i
Work out the value of the fraction as a decimal when n = 1 000 000.
ii
What fraction is equivalent to this decimal?
iii
How can you tell this from the original formula?
The nth term of a sequence is 3n + 7.
The nth term of another sequence is 4n – 2.
AU
These two series have several terms in common but only one term that is common and
has the same position in the sequence.
Without writing out the sequences, show how you can tell, using the expressions for the
nth term, that this is the 9th term.
5! means factorial 5, which is 5 × 4 × 3 × 2 × 1 = 120.
7! means 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
a
Calculate 2!, 3!, 4! and 6!.
b
If your calculator has a factorial button, check that it gives the same answers as you get
for part a. What is the largest factorial you can work out with your calculator before
you get an error?
Finding the nth term of a linear sequence
In a linear sequence the difference between one term and the next is always the same.
For example:
2, 5, 8, 11, 14, … difference of 3
The nth term of this sequence is given by 3n – 1.
Here is another linear sequence.
5, 7, 9, 11, 13, … difference of 2
The nth term of this sequence is given by 2n + 3.
So, you can see that the nth term of a linear sequence is always of the form An + b, where:
•
A, the coefficient of n, is the difference between each term and the next term (consecutive
terms)
•
b is the difference between the first term and A.
436 UNIT 2