Question

The sum of all even natural numbers between 1 and 81 is:

Answer 1

Answer:

1640

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Answer 2

The sum of all even natural numbers between 1 and 81 is 1640.

Step-by-step explanation:

To find : The sum of all even natural numbers between 1 and 81 is ?

Solution :

Th even natural number is in the form 2,4,6,8,....80 forming an arithmetic progression.

Where, first term is a=2

Common difference is d=2

Last term is l=80

The last term formula is

$l=a+(n-1)d$

$80=2+(n-1)2$

$(n-1)2=78$

$n-1=39$

$n=40$

The sum formula of A.P is given by,

$S_n=\frac{n}{2}[a+l]$

$S_{40}=\frac{40}{2}[2+80]$

$S_{40}=20[82]$

$S_{40}=1640$

Therefore, the sum of all even natural numbers between 1 and 81 is 1640.

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