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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Next, Vishnu made a pattern for the number he thought of. Try to find his number.

Example 11: Given below are some numbers arranged in some patterns. Find the sum of the
numbers in each of the below figures.

125 125
125
125
125
250
125
125 250 250
500 125
(a) (b) 125 250 500 100 500 250
125
125 500
250 250 125
125
250 125
125
125 125 125
Solution: We know that repeated addition means multiplication. So, we find:
(a) Sum of the numbers = 44 × 1 + 20 × 5 = 144

(b) Sum of the numbers = 18 × 125 + 8 × 250 + 4 × 500 + 100
= 2250 + 2000 + 2000 + 100 = 6350

Think and Answer

Choose a number between 150 and 200. Make a pattern to show the number.

Conjecture

A Conjecture is a mathematical statement that has not been proved yet. Conjecture is based on
observation of a pattern. It is an important step in problem-solving. A conjecture once proved
becomes a theorem.

Let’s generalise how a pattern helps in making conjectures. Here is a triangle known as the Pascal
Triangle named in honour of the great mathematician and physicist Blaise Pascal (1623–1662).
However, Blaise Pascal was not the first who designed this triangle. In India, Meru Prastar
(Pascal triangle) was known in 200 BCE. This triangle is symmetrical and we can visualise many
different number patterns inside it, but right now our main concern is to delve into the meaning
of conjecture.

87 Number Play