Page 181 - New Medley 5 Semester 2

That means, each square number is a sum of two consecutive triangular

numbers. Can you find the 7th square number and hence, split it into two
triangular numbers?

EXERCISE 8.3

A. 1. Observe the pattern and find the number of matchsticks required to

make 9th and 7th patterns respectively.

...

2. How many matchsticks will you need to make 6th and 10th patterns
respectively?

...

B. Find the sum of the following patterns.

1. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
2. 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20

3. 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44

4. 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50

[Hint: Use the concept of triangular numbers for adding given natural
numbers.]

C. 1. Compute the 11th, 15th and 31st triangular numbers.

2. Find the 12th, 16th and 30th square numbers and split them into two
triangular numbers.

3. 6 is a number which can be expressed as a line segment, triangle and a
rectangle.

Line segment Triangle Rectangle

Find the next two numbers that can be shown in the above shapes.

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