Lab Manual: Sum of Odd Natural Numbers - Class 10 PDF Download

Objective

Prerequisite Knowledge

• Natural numbers (i.e. counting numbers  e.g., 1, 2, 3, 4, …)
• Odd natural numbers (Natural numbers which are not divisible by 2  i.e.  1, 3, 5, …)
•  Even natural numbers (Natural numbers which are divisible by 2  i.e.  2, 4, 6,…)
• Formula to find the n ‘ term of an AP i.e.,
  a_n = a+ (n -1) d
  where a → first term,    d→ common difference,   n → no. of terms
• For odd natural numbers 1,3,5,…, term is
  a_n =1 + (n - 1). 2 = (2n - 1)
• Area of squares.

Materials Required
Squared papers, sketch pens, pencil, a pair of scissors, geometry box, fevicol, white drawing sheets

Procedure

• Take a squared chart paper of size n units X n units (Take n - 9).
  
• Paste it on a white sheet.
• Colour the internal squares with different 9 colours as shown in the fig. (i).
  
• Put a black dot on each of the internal coloured squares as shown in fig.(ii)
  

Observation

Result
The sum of first n odd natural numbers is n i.e., 1 + 3 + 5 + 7 + … + (2» —1) = n

Learning Outcome
Through this activity students are able to find that the sum of first n odd natural numbers n²  i.e., ∑(2n−1) =n²

Activity Time

• Find out the sum of first fifteen odd natural numbers with the help of above activity and verify the result using the formula ∑(2n−1) = n²
• Find the sum of (11 + 13 + …+21) using the result of this activity.