Find the sum of first n odd natural numbers.Find the sum of all odd numbers between (i) 0 and 50 (ii) 100 and 200.
Answers
Answer:
Sum of all odd numbers between 0 and 50 are 625
Sum of all odd numbers between 100 and 200 are 7500.
Step-by-step explanation:
Given :
(i) Sum of all odd numbers between 0 and 50 are 1, 3, 5 ,7 ,.........49
Here, a = 1, an,(l) = 49 , d = 3 - 1 = 2
By using the formula ,an = a + (n - 1)d
49 = 1 + (n - 1) 2
49 - 1 = 2n - 2
48 + 2 = 2n
50 = 2n
n = 50/2
n = 25
By using the formula ,Sum of nth terms , Sn = n/2 [a + l]
S25 = 25/2 [1 + 49]
S25 = 25/2 × 50
S25 = 25 × 25
S25 = 625
Hence, Sum of all odd numbers between 0 and 50 are 625
(ii) Sum of all odd numbers between 100 and 200 are 101, 103,105 ,107 ,.........199
Here, a = 101, an, (l) = 199, d = 103 - 101 = 2
By using the formula ,an = a + (n - 1)d
199 = 101 + (n - 1) 2
199 - 101 = 2n - 2
98 + 2 = 2n
100 = 2n
n = 100/2
n = 50
By using the formula ,Sum of nth terms , Sn = n/2 [a + l]
S50 = 50/2 [101 + 199]
S50 = 25 × 300
S50 = 7500
Hence, Sum of all odd numbers between 100 and 200 are 7500.
HOPE THIS ANSWER WILL HELP YOU….
Answer:
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
Sn=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.