# Understanding Number Sequences

A number Sequence or progression is an ordered list of numbers defined by a pattern or rule. The numbers in the sequence are said to be its numbers or terms. A sequence that continues indefinitely is called an infinite sequence. A sequence that ends is called a finite sequence.

For example, \( 2, 5, 8, 11, … \) form an infinite number sequence. The first term is \( 2 \); the second term is \( 5 \); the third term is \( 8 \), and so on. The description of this pattern in words could be “The sequence starts at \( 2 \), and each term is \( 3 \) more than the previous term.” Thus the fifth term is \( 14 \), and the sixth term is \( 17 \). The number sequence \( 2, 5, 8, 11, 14, 17 \), which terminates with the sixth term, is finite.

## Practice Questions of Number Sequence

### Question 1

Write down the first four terms of the number sequence if you start with \( 5 \) and add \( 6 \) each time.

\( \begin{aligned} \displaystyle

T_1 &= 5 \\

T_2 = 5 + 6 &= 11 \\

T_3 = 11 + 6 &= 17 \\

T_4 = 17 + 6 &= 23 \\

\therefore 5, 11, 17, 23

\end{aligned} \)

### Question 2

Write down the first five terms of the number sequence if you start with \( 50 \) and subtract \( 3 \) each time.

\( \begin{aligned} \displaystyle

T_1 &= 50 \\

T_2 = 50-3 &= 47 \\

T_3 = 47-3 &= 44 \\

T_4 = 44-3 &= 41 \\

T_5 = 41-3 &= 38 \\

\therefore 50, 47, 44, 41, 38

\end{aligned} \)

### Question 3

Write down the first three terms of the number sequence if you start with \( 4 \) and multiply by \( 3 \) each time.

\( \begin{aligned} \displaystyle

T_1 &= 4 \\

T_2 = 4 \times 3 &= 12 \\

T_3 = 12 \times 3 &= 36 \\

\therefore 4, 12, 36

\end{aligned} \)

### Question 4

Write down the first three terms of the number sequence if you start with \( 72 \) and divide by \( 2 \) each time.

\( \begin{aligned} \displaystyle

T_1 &= 72 \\

T_2 = 72 \div 2 &= 36 \\

T_3 = 36 \div 2 &= 18 \\

\therefore 72, 36, 18

\end{aligned} \)

### Question 5

Write a description of a number sequence; \( 11, 14, 17, 20, … \)

It starts at \( 11 \), and each term is \( 3 \) more than the previous term.

### Question 6

Write a description of a number sequence; \( 2, 6, 18, 54, … \)

It starts at \( 2 \), and each term is \( 3 \) times the previous term.

### Question 7

Find the next two terms of a number sequence; \( 95, 91, 87, 83, … \)

\( \begin{aligned} \displaystyle

T_5 = 83-4 &= 79 \\

T_6 = 79-4 &= 75

\end{aligned} \)

### Question 8

Find the next two terms of a number sequence; \( 2, 4, 7, 11, … \)

\( \begin{aligned} \displaystyle

T_2 = 2 + 2 &= 4 \\

T_3 = 4 + 3 &= 7 \\

T_4 = 7 + 4 &= 11 \\

T_5 = 11 + 5 &= 16 \\

T_6 = 16 + 6 &= 22

\end{aligned} \)

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