Find the sum of all odd numbers between
(i) 0 and 50
(ii) 100 and 200
Answers
Sum of all odd numbers between 0 and 50 & 100 and 200.
1. To find out the sum of odd numbers between 0 and 50& 100 and 200 we should find out the number of odd terms in between 0&50.
2. Sequence is 1,3,5,7....49
3. Here a=1 ,l= 49 ,d=2
4. From, l= a +(n-1)d by substituting values we get, 49= 1+(n-1)2
5.we get , n=25.
6.From the formula ,Sn = n/2 (a+l)
Sn = 25/2 (49+1)
Sn = 25(25)
Sn = 625.
7.Sum of all odd numbers between 0 and 50 is 625.
8. Now to find number of odd numbers in between 100 and 200,
Sequence is 101,103,105,....199.
9.a=101, l=199, d=2
10. l= a+(n-1)d
199= 101+(n-1)2
n=50.
11. For sum of all odd numbers,Sn = n/2 (a+l)
Sn = 50/2 (199+101)
Sn= 7500.
Answer:
a + ( n - 1) d = an
=> 1 + ( n - 1) 2 = 49
=> ( n - 1) 2 = 48
=> ( n - 1) = 24
=> n = 25.
So,
Sn = n/2 × ( a +l)
= 25 /2× ( 1 +49)
= 25 /2 × 50
= 25 ×25
= 62