Question

Find the sum of first n even number

Answer 1

Answer:

1 is the answer to this question

Answer 2

Step-by-step explanation:

Let the sum of first n even numbers is Sn

Sn = 2+4+6+8+10+…………………..+(2n) ……. (1)

By Arithmetic Progression, we know, for any sequence, the sum of numbers is given by;

Sn=1/2×n[2a+(n-1)d] ……..(2)

Where,

n = number of digits in the series

a = First term of an A.P

d= Common difference in an A.P

Therefore, if we put the values in equation 2 with respect to equation 1, such as;

a=2 , d = 2

Let, last term, l = (2n)

So, the sum will be:

Sn = ½ n[2.2+(n-1)2]

Sn = n/2[4+2n-2]

Sn = n/2[2+2n]

Sn = n(n+1)

Sum of n even numbers = n(n+1)

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