Question

plzzz solve it help me.. ​

Answer 1

Answer :

$\large{\star\:\:\boxed{\bf{S_{250}\:=\:62500}}\:\:\star}$

Explanation :

$\dag$ Given  : –

A.P.  :- 1 , 3 , 5 , 7 , . . .

where a = 1 , d = 2 and n = 499 .

$\dag$ To Find  : –

Sum of all the Terms of this A.P.

$\dag$ Formulae Applied :–

$\boxed{\star\:\:\bf{S_{n}\:=\:\dfrac{n}{2}\:\times\:(a\:+\:l) }\:\:\star}$

$\boxed{\star\:\:\bf{a_n\:=\:a\:+\:(n\:-\:1)d }\:\:\star}$

$\dag$ Solution : –

☆ Firstly , we will find the number of Terms :

We have ,

a = 1

d= 2

n = 250

Putting these values in the Formula :

$\rightarrow\sf{a_n\:=\:a\:+\:(n\:-\:1)d}$

$\rightarrow\sf{a_{250}\:=\:1\:+\:(250\:-\:1)(2)}$

$\rightarrow\sf{a_{250}\:=\:1\:+\:(249\:\times\:2)}$

$\rightarrow\sf{a_{250}\:=\:1\:+\:498}$

$\rightarrow\bf{a_{250}\:=\:499}$

★ Then , we have to find now the Sum of all the Terms of this A.P. :

We have ,

a = 1

l = 499

n = 250

Putting these values in the Formula :

$\rightarrow\sf{S_{n}\:=\:\dfrac{n}{2}\:\times\:(a\:+\:l) }$

$\rightarrow\sf{S_{250}\:=\:\dfrac{250}{2}\:\times\:(1\:+\:499) }$

$\rightarrow\sf{S_{250}\:=\:\dfrac{250}{2}\:\times\:500 }$

$\rightarrow\sf{S_{250}\:=\:250\:\times\:250 }$

$\rightarrow\boxed{\bf{S_{250}\:=\:62500 }}$

∴ The Sum of First 250 odd Natural Numbers is 62500 .

Answer 2

Answer:

The number series 1, 3, 5, 7, 9, .  .  .  .  , 499.

The first term a = 1

The common difference d = 2

Total number of terms n = 250

apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 250/2 x (1 + 499)

= (250 x 500)/ 2

= 125000/2

1 + 3 + 5 + 7 + 9 +..........+ 499 = 62500

Therefore, 62500 is the sum of first 250 odd numbers.

hope this helps you