You'll have found by now that algebra forms a major part of KS3 Maths. In algebra letters are used in place of numbers. The letter *n* (usually in italics) is often used to indicate the position of a term in a sequence. We call this the '*n*th' term.

Finding the rule for a number pattern is usually quite easy but can sometimes be a bit harder. One famous pattern is the Fibonacci sequence. This describes a spiral pattern and is very common in nature. The rule for the Fibonacci sequence is to add the previous two numbers to find the next. The *n*th term for this would be... advanced mathematics. Don't worry about that just yet!

Here's an easier example. If a sequence begins with 5 and goes up in twos thereafter, the *n*th term of that sequence would be 2n + 3 (2 x 1 + 3 = 5, 2 x 2 + 3 = 7, 2 x 3 + 3 = 9 etc.). This can be a little difficult to grasp but work through this quiz (and read the helpful comments!) and you will soon get the idea.

1.

The *n*th term of a sequence is given by 3n + 1. What is the numeric value of the 1^{st} term?

3

4

6

9

2.

The *n*th term of a sequence is given by 3n + 1. What is the numeric value of the 3^{rd} term?

4

6

8

10

The answer can be found as follows: (3 x 3) + 1

3.

What is the *n*th term of the sequence 6, 11, 16, 21?

5n

5n + 1

5n + 5

n + 5

(5 x n) + 1

4.

What is the next number in this sequence: 1, 8, 27?

35

36

54

64

These are known as cube numbers. The 1^{st} number in the sequence is 1 x 1 x 1; the 2^{nd} number is 2 x 2 x 2; the 3^{rd} number is 3 x 3 x 3 and the 4^{th} number will be 4 x 4 x 4

5.

The *n*th term of a sequence is given by 14n - 6. What is the numeric value of the 2^{nd} term?

8

20

22

24

(14 x 2) - 6

6.

The *n*th term of a sequence is (2n)^{2} + 1. What is the the numeric value of the 3^{rd} term?

33

35

37

39

(2 x 3)^{2} + 1

7.

The *n*th term of a sequence is (n + 1)^{2}. What is the the numeric value of the 4^{th} term?

20

25

30

35

(4 + 1)^{2}

8.

The *n*th term of a sequence is given by 3n + 1. What is the numeric value of the 8^{th} term?

12

13

25

50

We are told that we need the 8^{th} term. We put an 8 where the n is and then work it out: (3 x 8) + 1

9.

What is the next number in this sequence: 1, 1, 2, 3, 5, 8?

12

13

14

15

This is known as the Fibonacci sequence. To find each number you add together the two previous numbers. After 13 comes 21 (8 + 13) and then comes 34 (21 + 13)

10.

What is the next number in this sequence: 1, 4, 9, 16?

18

20

22

25

These are known as square numbers. The 1^{st} number in the sequence is 1 x 1; the 2^{nd} number is 2 x 2; the 3^{rd} number is 3 x 3 etc.

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^{st}term the value of n will be 1 and therefore the answer can be found as follows: (3 x 1) + 1