Respuesta :
Answer:
The sum of even numbers between 1 and 100 is 2550.
Step-by-step explanation:
To find : Add the even numbers between 1 and 100?
Solution :
The even numbers from 1 to 100 is 2,4,6,...,100 form an arithmetic progression,
The first term is a=2
The common difference is d=2
The last term is l=100
First we find the number of terms given by,
[tex]l=a+(n-1)d[/tex]
[tex]100=2+(n-1)2[/tex]
[tex]100=2+2n-2[/tex]
[tex]2n=100[/tex]
[tex]n=\frac{100}{2}[/tex]
[tex]n=50[/tex]
The sum formula of A.P is
[tex]S_n=\frac{n}{2}[a+l][/tex]
Substitute the values in the formula,
[tex]S_{50}=\frac{50}{2}[2+100][/tex]
[tex]S_{50}=25\times 102[/tex]
[tex]S_{50}=2550[/tex]
Therefore, The sum of even numbers between 1 and 100 is 2550.
