Question

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

Answer 1

Answer:

Hence the sum of all odd numbers between 0 and 50, is 625

Step-by-step explanation:

We know that the first odd number between 0 and 50 is 1 and last odd number is 49.

So we solve this by Arithmetic Progression

Let first term of A.P. (a) = 1

Second term in A.P = 3

Common difference (d) = second term - first term

                                       = 3 - 1

d = 2

Last term of A.P. ( l ) = 49

Using formula-

$T_{n} = a + (n-1)d$

Where $T_{n} = last \ term \ of \  A.P.$

a = first term of A.P.

d = common difference

n = total term of A.P

But $T_{n} = 49$

a = 1, and d = 2

So,  

49 = 1 + (n - 1)×2

49 - 1 = 2n - 2

48 = 2n - 2

2n = 48 + 2

2n = 50

$n = \dfrac{50}{2}$

n = 25

So, there are 25 odd numbers between 0 and 50.

So, sum of these numbers-

Using formula-

$S_{n} = \dfrac{n}{2}[a + l]$

Where n = total terms in A.P.

a = first term of A.P

l = last term of A.P.

So, $S_{n} = \dfrac{25}{2}[1+49]$

                     = $\dfrac{25}{2}\times 50$

                     = 25 × 25

$S_{n} = 625$

Hence the sum of all odd numbers between 0 and 50, is 625

Answer 2

Refers to attachment ♡~