Question

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

Answer 1

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 2

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