Question

express 100 as a sum of 10odd number

Answer 1

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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)
              Sn = n/2x[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
Sn= 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.

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