Question

express 100 as sum of 10 odd natural number

Answer 1

Using Arithmetic Progression, we are going to express it.

Formula used: Sum of n odd numbers (odd or even or natural or whole, the answer is based on the difference between 2 successive terms in the series)
                              Sₓ = 1/2 x n[2a+(n-1)×d]

Series be 1,3,5,7,9,11... (odd numbers)
Total numbers n = 10
First number in the sequence a = 1
Difference between two successive terms d = 3-1 = 2

Sum of n odd numbers: Sₓ = 1/2 x n[2a+(n-1)×d]
                                      S₁₀ = 1/2 x 10[2(1)+(10-1)2]
                                      S₁₀ = 1/2 x 10[2+18]
                                      S₁₀ = 5(20)
                                      S₁₀ = 100

Hence, It is proved.