Question

Sum of all even numbers between 1 to 100

Answer 1

To find the sum of even numbers between 1 and 100, we can use the concept sum of n numbers in A.P.(arithmetic progression)

Here we need sum of 2,4,6,……..,98(between 1 and 100)

Now here First term = 2 difference= 2, n = 50

So now sum of these terms = n/2(2a+(n-1)d)

= 49/2(2*2+(50–1)2)

= 49/2(4+(49)*2)

= 49/2(4+98)

= 49/2(102)

= 49*51

=2550

This can also be done by : (sum of first 100 numbers - sum of odd numbers between 1 and 100) = sum of even numbers between 1 and 100.

Hope it helps you!!!

Answer 2

Answer:

The sum of all even numbers between 1 to 100 is 2550.

Step-by-step explanation:

As per the data given in the question,

We have,

even numbers between 1 to 100= 2,4,6,8...100

Since, it is even series so the last number will be 50th term.

and it is forming a AP with a=2, d=2 and n=50

So, applying AP sum formula here:

$=\frac{n}{2}(2a+(n-1)d) \\=\frac{50}{2}(2\times2+(50-1)\times2)\\=25(4+98)\\=25\times102\\=2550$

Hence, sum of all even numbers between 1 to 100 is 2550.

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