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Perfect Cubes and Consecutive Odd Numbers
Last updated at July 30, 2025 by Teachoo
Perfect Cubes - and its Patterns
Class 8 (Ganita Prakash & Old NCERT)
Chapter 1 Class 8 - A Square and a Cube (Ganita Prakash)
- Introduction
- Square Numbers
- Perfect Squares - and its Properties
- Perfect Squares - and its Patterns
- Square Root
- Smallest number multiply or divide to get perfect square
- Estimating Square Root
- Figure it out - Page 10, 11
- Cubic Numbers
- Perfect Cubes - and its Properties
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Perfect Cubes - and its Patterns
- Cube Root
- Smallest number multiply or divide to get perfect cube
- A pinch of History
- Figure it out - Page 16, 17
Transcript
Perfect Cubes and Consecutive Odd Numbers We have this pattern Can you figure out what it is? The text shows that for any whole number n, the value of n³ is equal to the sum of n consecutive odd numbers. 13 is the sum of 1 odd number: 1 = 13 23 is the sum of next 2 consecutive odd numbers: 3 + 5 = 8 = 23 33 is the sum of next 3 consecutive odd numbers: 7 + 9 + 11 = 27 = 33 43 is the sum of next 4 consecutive odd numbers: 13 + 15 + 17 + 19 = 64 = 43 We are given a question What is the sum of 91 + 93 + 95 + 97 + 99 + 101 + 103 + 105 + 107 + 109 without doing the calculation? To find the answer, you simply need to count how many consecutive odd numbers are in the series. There are 10 numbers being added. According to the pattern, this sum is equal to 10³, which is 1000.
