Question

Find the sum of all odd numbers between
(i) 0 and 50 (ii) 100 and 200.

Answer 1

1-Odd number between 0 and 50 are 1,3,5,7,9.....49
l=a+(n-1)d
49=1+(n-1)2
2n-2=48
2n=50
n=50/2
n=25
$S_n$ = $\frac{n}{2}$ (a+l)
=25/2(1+49)
=25/2(50)
=25(25)
=625.
Therefore the sum of all odd numbers between 0 and 50 is 625.




2-
101,103,105...........199

an = 199 a = 101 d= 2

a_n= a+ (n-1)d

199 = 101 +(n-1) 2

199-101 = (n-1)2

98/2 = n-1

49 +1 = n

so, n= 50

$S_n$ = $\frac{n}{2}$ (a+l)

= 50/ 2 (101+199)

= 25 x 300

= 7500