Page 213 - Math Smart - 7

CHAPTER 9.2

In this chapter
Generating Number Pupils should be able to:

• describe the general
Sequences and Finding term in a number

sequence
• generate sequences
the General Term from spatial patterns

We can use a formula to describe the relationship between the numbers in a
sequence. We do this by comparing the terms in the number sequence to its
position in the sequence.
2, 4, 6, 8, 10, ... is a sequence of positive even numbers.

We can use Ti, T2, T3,... to denote each term in the sequence.

Ti (1"term) = 2
T2 (2"'^ term) = 4
T3 term) = 6
T4 (4^^ term) = 8
T5 {5^" term) = 10
So, Tp represents the term or general term.

We can present the sequence in a table.

Position of term in
1 2 3 4 5 ... n
the sequence, n
2 X 1 2X2 2X3 2X4 2X5 2X n
Term, In
= 2 = 4 = 6 = 8 = 10 = 2n

We see that the term is always twice the position of the term. We say the
general term in the sequence is 2n. So, In = 2/i. n is the variable representing
the position of the term.

So, to find the 110*^" term in the sequence, we use the formula In = 2n and get
Tiio = 2 X 110 = 220.