Question

Derive the formula for the sum of first n even natural numbers

Answer 1

Step-by-step explanation:

Sum of First n Natural Numbers. ... Clearly, it is an Arithmetic Progression whose first term = 1, last term = n and number of terms = n. Therefore, S = n2(n + 1), [Using the formula S = n2(a + l)] Solved examples to find the sum of first n natural numbers. 1.

Answer 2

Sum Formula = n/2 {2a + (n-1)d}

For even numbers, a=2 and d=2

So, new formula is

Sum= n/2{2(2) + (n-1)2}

= n/2{4 + 2n - 2}

= n (2+2n)

2

= n × 2(1+n)

2

= n(n+1)

Hope it helps!!! :)