Question

Find the sum of the odd numbers between 0 and 50.

NCERT Class X
Mathematics - Mathematics

Chapter _ARITHMETIC PROGRESSIONS

Answer 1

First odd number is 1
Last odd number is 49
a = 1 an or I = 49 ,common difference d= 2.
an = a+(n-1)d
=1+(n-1)2 = 49
=1+2n-2 =49
=2n-1 =49
=2n=49+1
=2n=50
n=25
sn=n/2(1+49)
=25/2(1+49)
=25/2* 50
25 *25 = 625
therefore sum of all odd integers between 0 to 50 is 625.

Answer 2

HEY THERE!!!



Let to be First term 'a' and Common difference 'd'.



Firstly,all odd numbers between 0 and 50 which are given below in the form of Arithmetic Sequence or Progression;



1,3,5,7,9,11.....49



Now, Write in Summation of Arithmetic Sequence or Progression;-




Let Sn = 1+3+5.....49



Here,



First term (a)= 1



Common difference (d)=2



Last terms= 49




Let the number of terms be 'n'



Then,



Tn =a+(n-1)d



Substitute the value of the Required terms in Above Formula;-



Tn =a+(n-1)d



=> 1+(n-1)2 = 49



=> 1+2n-2= 49



=> -1+2n=49



=>2n=49+1



=> 2n=50



=> n=50/2



=> n=25



Now, Using Formula of Summation of terms which known as Sum of terms;-



Sn=n/2(a+l)


=> 25/2(1+49)

=> 25/2(50)

=> 25×25

=> 625



Hence, 625 are the sum of all odd numbers between 0 and 50.