Observe the following pattern
$1 + 3 = 2^2$
$1 + 3 + 5 = 3^2$
$1+3 + 5 + 7 = 4^2$
and write the value of $1 + 3 + 5 + 7 + 9 +…………$ upto $n$ terms.

Given:

$1 + 3 = 2^2$

$1 + 3 + 5 = 3^2$

$1+3 + 5 + 7 = 4^2$

To do:

We have to write the value of $1 + 3 + 5 + 7 + 9 +…………$ upto $n$ terms.

Solution:

We can observe that sum of first two odd numbers is $2^2$

Sum of first three odd numbers is $3^2$

Sum of first four odd numbers is $4^2$

This implies,

Sum of first $n$ odd numbers $=n^2$.

Therefore,

$1 + 3 + 5 + 7 + 9 +…………$ upto $n$ terms is $n^2$.

Tutorialspoint

e

Updated on: 10-Oct-2022

51 Views

Kickstart Your Career

Get certified by completing the course

Get Started