Courses
Courses for Kids
Free study material
Free LIVE classes
More
LIVE
Join Vedantu’s FREE Mastercalss

Find the sum of first n odd numbers.

Answer
VerifiedVerified
365.7k+ 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.
Last updated date: 29th Sep 2023
•
Total views: 365.7k
•
Views today: 10.65k