Question
Download Solution PDFWhat is the sum of first n odd natural numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Sum of the first n terms of an AP = S = \(\rm \frac{n}{2}\)[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 = \(\rm \frac{n}{2}\)[2a + (n − 1) × d]
Therefore, Sn = \(\rm \frac{n}{2}\)[2 × 1 + (n − 1) × 2] = \(\rm \frac{n}{2}\) × 2n = n2
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