Discovering algebra is a big part of KS3 Maths. In algebra, we use letters instead of numbers. For example, the letter 'n' (often in italics) shows where a term is in a sequence, and we call it the 'nth' term.

Figuring out the rule for a number pattern can be easy or a bit tricky. Have you heard of the Fibonacci sequence? It creates a cool spiral pattern seen in nature. The rule: add the previous two numbers to find the next one. The nth term? Well, that's for advanced maths - no need to worry about that just yet!

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1 .

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

2 .

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

3 .

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

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

4 .

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}

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 .

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)

7 .

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

8 .

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.

9 .

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

5n

5n + 1

5n + 5

n + 5

(5 x n) + 1

10 .

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

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