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Question 11 Mark
Find your own patterns or relations in and among the sequences in Table 1. Can you explain why they happen with a picture or otherwise?
Answer
Given table is as
1, 1, 1, 1, 1, 1, ... (All 1's)
1, 2, 3, 4, 5, 6, 7, ... (Counting numbers)
1, 3, 5, 7, 9, 11, 13, ... (Odd numbers)
2, 4, 6, 8, 10, 12, 14, ... (Even numbers)
1, 3, 6, 10, 15, 21, 28, ... (Triangular numbers)
1, 4, 9, 16, 25, 36, 49, ... (Squares)
1, 8, 27, 64, 125, 216, ... (Cubes)
1, 2, 3, 5, 8, 13, 21, ... (Virahanka numbers)
1, 2, 4, 8, 16, 32, 64, ... (Powers of 2)
1, 3, 9, 27, 81, 243, 729, ... (Powers of 3)
From the above table, we see that
On adding the counting numbers up and turn down we get the square numbers.
Image
and so on.
Thus, counting number is relate with square numbers.
Also, we see triangular numbers added together for square numbers.
Image
Also, we can look following patterns,
Image
Here, we get a sequence of square of triangular numbers.
Thus, we can say that sequence relate to each other.
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Question 41 Mark
How has mathematics helped propel humanity forward? (You might think of examples involving: carrying out scientific experiments; running our economy and democracy; building bridges, houses or other complex structures; making TVs, mobile phones, computers, bicycles, trains, cars, planes, calendars, clocks, etc.)
Answer
Mathematics is an essential part of our life and helps us to understand the world in different way. It teaches us to analyse data, identify patterns and develop creative solutions to complex problems. These skills are essential in today's fast paced, data driven world and are highly valued in many industries, including finances, healthcare and technology.
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Question 51 Mark
Can you think of other examples where mathematics helps us in our everyday lives?
Answer
Mathematics helps us in managing money, preparing food, figuring out distance, time and cost of travel, baking, home decorating etc. 
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1 Marks Question - MATHS STD 6 Questions - Vidyadip