Question

Find the sum of odd numbers between 0 and 50

Answer 1

Answer:

sum of all odd number between 1to50

= (50/2)square

=(25)square

=625

Answer 2

★ GiveN :

A.P : 1, 3, 5, 7, 9 ........ 49

First term (a) = 1

Common Difference (d) = 2

Last term (An or L) = 49

$\rule{200}{1}$

★ To FinD :

We have to find the sum of odd numbers between 0 and 50 ?

$\rule{200}{1}$

★ SolutioN :

Firstly, we will calculate the number of terms.

So,

$\Large{\implies{\boxed{\boxed{\sf{A_n = a + (n - 1)d}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow 49 = 1 + (n - 1)2} \\ \\ \sf{\dashrightarrow 49 = 1 + 2n - 2} \\ \\ \sf{\dashrightarrow 49 = 2n - 1} \\ \\ \sf{\dashrightarrow 2n = 49 + 1} \\ \\ \sf{\dashrightarrow 2n = 50} \\ \\ \sf{\dashrightarrow n = \frac{\cancel{50}}{\cancel{2}}} \\ \\ \sf{\dashrightarrow n = 25} \\ \\ \Large{\implies{\boxed{\boxed{\sf{n = 25}}}}}$

$\rule{150}{2}$

Now,

$\Large{\implies{\boxed{\boxed{\sf{S_n = \frac{n}{2}(a + L)}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow S_{50} = \frac{25}{2} (1 + 49)} \\ \\ \sf{\dashrightarrow S_{50} = \frac{25}{\cancel{2}} \times \cancel{50}} \\ \\ \sf{\dashrightarrow S_{50} = 25 \times 25} \\ \\ \sf{\dashrightarrow S_{50} = 625} \\ \\ \Large{\implies{\boxed{\boxed{\sf{S_{50} = 625}}}}}$