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}

Induction Made Simple: The Ultimate Guide

“Induction Made Simple: The Ultimate Guide” is your gateway to mastering the art of mathematical induction, demystifying a powerful tool in mathematics. This ultimate guide…

General Term of a Number Sequence

Sequences may be defined in one of the following ways: Consider the illustrated pentagons and matches below: A pentagon is made using matches. By adding…

Number Sequences – Comprehensive Explanations and Clear Examples

In $\textit{sequences}$, it is important that we can; A $\textit{number sequence}$ is an ordered list of numbers defined by a rule. The numbers in the…

Probability with Two-Digit Numbers by Dice

Transcript Two dice are thrown. One yellow and one white. Let y be the uppermost number on the yellow die and w be the uppermost…