What is the sum of first n odd natural numbers?

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Airforce Group X 4 November 2020 Memory Based Paper
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  1. n2 - 1
  2. n2
  3. n3

Answer (Detailed Solution Below)

Option 2 : n2
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Detailed Solution

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Concept:

Sum of the first n terms of an AP = S = [2a + (n − 1) × d]

Where, a = First term, d = Common difference, n = number of terms


Calculation:

To find:  Sum of first n odd natural numbers

Odd natural number starts from 1.

The series of odd natural numbers is 1 , 3 , 5 , 7, 9 ...

Above series is in AP                      (∵ Common difference are same)

a = First term = 1, d = Common difference = 2

As we know, Sn =  [2a + (n − 1) × d]

Therefore, Sn =  [2 × 1 + (n − 1) × 2] =  × 2n = n2

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