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Q01 |
- Diagram : Squares in squares
- Q02 | - How many squares in the diagram ?
- Q03 | - Definition
- Q04 | - Size-3 square containing 4 size-2 square
- Q05 | - sequences
- Q06 | - Patterns
- Q02 | - How many squares in the diagram ?
Q01. Diagram : Number of squares
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Q02. How many squares in the diagram
Answer
- Number 1 square = 01 : It consists of 25 small squares
- Number 2 square = 04 : Each square contains 16 small squares
- Number 3 square = 09 : Each square contains 09 small squares
- Number 4 square = 16 : Each square contains 04 small squares
- Number 5 square = 25 : Each square contains 01 small squares
- Total squares 1 + 4 + 9 + 16 + 25 = 55 squares.
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Q03. Definition
What is the definition ?
- Size-1 square : The smallest square and stands for 1^2
- Size-2 square : It includes 04 size-1 squares and stands for 2^2
- Size-3 square : It includes 09 size-1 squares and stands for 3^2
- Size-4 square : It includes 16 size-1 squares and stands for 4^2
- Etc.
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Q04. Why size-3 square has 4 size-2 square ?
Diagram
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Q05. What is the sequence ?
The sequence
- It is the number square sequence : 1, 4, 9, 16, 25, .......
- T(n) = nth term = n^2
- S(n) = Sum of n terms = n*(n + 1)*(2*n + 1)/6
- Subject | Sum[n^2] = n*(n + 1)*(2*n + 1)/6
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Q06. Sequence Patterns
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.... 1 .... 4 ........ 9 ......... 16
.... * .. * * .... * * * .... * * * *
......... * * .... * * * .... * * * *
.................. * * * .... * * * *
............................. * * * *
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