Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store

Find the sum of first n odd numbers.

seo-qna
Last updated date: 17th Apr 2024
Total views: 426k
Views today: 8.26k
Answer
VerifiedVerified
426k+ views
Hint- The formula for the sum of an A.P is${{\text{S}}_n} = \dfrac{n}{2}\left( {2{a_1} + \left( {n - 1} \right)d} \right)$, where n is number of terms.

We have to find out the sum of first n odd numbers.
$ \Rightarrow 1 + 3 + 5 + 7 + .........................n{\text{ terms}}{\text{.}}$
As we see that $\left( {1,3,5,7..............n} \right)$makes an A.P
Where, number of terms of the series${\text{ = n}}$
             First term $\left( {{a_1}} \right) = 1$
            Common difference$\left( d \right) = \left( {3 - 1} \right) = \left( {5 - 3} \right) = 2$
Now apply the formula of sum of an A.P
$
  {{\text{S}}_n} = \dfrac{n}{2}\left( {2{a_1} + \left( {n - 1} \right)d} \right) \\
   \Rightarrow {{\text{S}}_n} = \dfrac{n}{2}\left( {2 \times 1 + \left( {n - 1} \right)2} \right) \\
   \Rightarrow {{\text{S}}_n} = \dfrac{n}{2}\left( {2 + \left( {n - 1} \right)2} \right) = n\left( {1 + n - 1} \right) = {n^2} \\
$

Note- In such types of questions always remember the basic formulas of an A.P which is stated above, then from the given condition calculate the values of first term and common difference, then apply the formula of sum of an A.P we will get the required sum of first n odd numbers.