Question

find the sum of first 250 odd natural numbers ?
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Answer 1

Answer:

step 1 Address the formula, input parameters & values.

Input parameters & values:

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

step 2 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.

Step-by-step explanation:

The below workout with step by step calculation shows how to find what is the sum of first 250 odd numbers by applying arithmetic progression. It's one of the easiest methods to quickly find the sum of given number series.

Answer 2

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 .