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Question

The sum of first n odd natural numbers is


A

2n+1

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B

n2

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C

n21

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D

n2+1

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Solution

The correct option is B

n2


Explanation for Correct answer:

Arithmetic Progression

  1. Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
  2. In AP, we will come across some main terms, which are denoted as:

a. First term (a)
b. Common difference (d)
c. nth Term (an)
d. Sum of the first n terms (Sn)

Option (b): n2

The Sum of an AP is: S=n2×(2a+(n1)d)

The sum of first n odd natural numbers are given by 1,3,5,7,9(2n1) and this forms an AP.

a=1

d=2

tn=(2n1)

Sum of first od numbers are calculated as follow:

S=n2×(2a+(n1)d)S=n2×(2+2n2)S=n2×2nS=n2

Hence, Option (b) is the correct answer.

Explanation for incorrect answer:

Option (a): 2n+1

Option (c): n21

Option (d): n2+1

As the sum of first n odd natural numbers is n2 as determined above.

Thus, option (a), (c) and (d) are incorrect answers.

Hence, option (b) is the correct answer.


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