Question

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

Answer 1

Answer:

625

Step-by-step explanation:

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.

Answer 2

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Odd numbers are classified as any number that is not divisible by two. In other terms, a number in the form of 2k+1, where k ∈ integers(Z) are called odd numbers. The sum of two odd numbers is always even.

The list of odd numbers between 0 and 50 are

1,3, 5, 7, 9, ….49.

To find the sum of all the odd numbers between 0 – 50 we use the theory of arithmetic progression.

a = 1

d = 2

n = ?

an = 49

an = a + (n-1)d

49 = 1 + (n – 1) × 2

49 = 1 + 2n – 2

49 = 2n -1

50 = 2n

n = 25

The sum of all odd numbers between 0 and 50 can be calculated using the formula

Sn = n/2 (a +an)

Sn = 25/2 (1 + 49)

Sn = 25/2 (50)

Sn=625