Recognising Number Sequences
Consider the number sequence 4, 7, 10, 13, 16, 19, . . .
The first term in the sequence is 4, and the second term is 7.
How can we know the 'pattern' to the next number after 19 ?
Usually, we look at the first three numbers 4, 7 and 10, and check for a pattern.
The most common way is to check for the pattern is to find the difference between them.
= > 4 to 7 = 3, 7 to 10 = 3
=> the next sequence is adding 3.
Therefore the number after 19 is 19 + 3 = 22.
Example
Find the next three terms of the number sequence 3, 7, 11, 15, …
7 -3 = 4, 11 - 7 = 4 (Step 1 : Find sequence pattern with first 3 numbers)
+4 is the pattern (Step 2 : Add to sequence 'pattern'
15 + 4 = 19, 19 + 4 = 23, 23 + 4 = 27
The next three terms are 19, 23 and 27.
Evaluating the "nth" Term (the "position" in the sequence)
A formula or Expression can be given to a number sequence.
Then we can find the number in the sequence by substituting or "putting" the value into the Expression.
Example
A number sequence has the expression 2n + 3. Find the first three terms.
First term => n = 1
5n + 2
When n = 1, (Step 1 : Write Expression, and substitute )
5n + 2 =5(1) + 2 (Step 2 : Substitute value to find answer)
= 7
When n = 2,
5n + 2 = 5(2) + 3 =13
When n = 3,
5n + 2 = 5(3) + 3 = 18
The first 3 terms are 7, 13, 18
Example
The nth term of a number sequence is 4n - 2. Find the 6th and 7th term.
4n - 2 (Step 1 : Write Expression, and substitute )
When n = 6,
4n - 2 = 4(6) - 2 = 22 (Step 2 : Substitute value to find answer)
When n = 7,
4n - 2 = 4(7) - 2 = 28 - 2 = 26
The 6th term is 22 and the 7th term is 26
Example
The first 4 terms of a sequence are 4, 11, 18, 25
a. Find an expression for the nth term of this sequence
4 n + 7
Step 1 : Find the pattern
11 - 4 = 18 - 11 = 7 => pattern = +7
Step 2: Form the first term with ? + 7n = 4
1st term => n = 1
? + 7(1) = 4
Step 3: Write the Expression
nth term = -3 + 7n
Practice
1. Find the next three terms of the following number sequence
a. 1, 5, 9, 13, …
b. 7, 10, 13, 16,...
c. 102, 107, 112, 117, …
2. Nth term of a number sequence is 3n - 1
(a) Find the first three terms
(b) Find the 10th term
(c) Find the 99th term
3. Simplify 2x - 3(x - 2) [12/I/17/2/A]
3 5
4. Simplify 3x - 2x + 1 [14/II/17/8/A]
2 3
<< End of (1) Sec 2 Algebra NT/L1 and (2) Sec 1 NA >>
