Page 208 - ICSE Math 5

Exercise 15.3

1. Use the following codes to code the given messages.

A B C D E F G H I J K L M
26 25 24 23 22 21 20 19 18 17 16 15 14

N O P Q R S T U V W X Y Z
13 12 11 10 9 8 7 6 5 4 3 2 1

(a) KEEP YOUR CITY CLEAN (b) RESPECT YOUR ELDERS

2. Decode the following messages by using the codes given in the above question.
(a) 18 15 12 5 22 14 2 24 12 6 13 7 9 2

(b) 8 26 5 22 4 26 7 22 9 26 13 23 22 15 22 24 7 9 18 24 18 7 2

(c) 19 26 11 11 2 23 18 4 26 15 18

Triangular and Square Numbers

Every number sequence has at least one rule that helps us to find out how each number in
the sequence is obtained from the previous number. This also helps us to find the sequence in
triangular and square numbers. Let’s know about triangular and square numbers.

Triangular Numbers

Numbers that can be arranged as dots in the shape of a triangle are known as triangular numbers.
Look at the given triangular number sequence.

1, 3, 6, 10, …
We can identify the pattern rule by drawing dots that form a triangle.

1 1 + 2 = 3 (1 + 2) + 3 = 6 (1 + 2 + 3) + 4 = 10

Observe that the pattern is obtained by adding successive number of dots in a continuous manner.

Square Numbers

Numbers that can be arranged as dots in the shape of a square are called square numbers. Look
at the given square number sequence below.

1, 4, 9, 16, …

198