Question

find the sum of the first 5o even natural numbers​

Answer 1

Answer:

How to Find the Sum of First 50 Even Numbers?

The below workout with step by step calculation shows how to find what is the sum of first 50 even numbers by applying arithmetic progression. It's one of the easiest methods to quickly find the sum of given number series.

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 2, 4, 6, 8, 10, 12, . . . . , 100.

The first term a = 2

The common difference d = 2

Total number of terms n = 50

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 50/2 x (2 + 100)

= (50 x 102)/ 2

= 5100/2

2 + 4 + 6 + 8 + 10 + 12 + . . . . + 100 = 2550

Therefore, 2550 is the sum of first 50 even numbers.

Answer 2

The first 5 even natural numbers are

• 2
• 4
• 6
• 8
• 10

Now we have to add these to find the sum of first five even natural numbers.

So,

2 + 4 + 6 + 8 + 10 = 30

So, the sum of the first five natural even numbers is 30.

Now we will find the sum of the first 50 natural even numbers but in a lil bit different manner.

S=2+4+6+8+... up to 50 terms

a=2,d=4−2=2 and n=50

∴Sn=2n[2a+(n−1)d]

=250[2×2+(50−1)×2]

=50[2+49]

=50×51=2550

∴ Sum of 50 even natural numbers=2550

SO, I HOPE YOU HAVE UNDERSTOOD..☺️