Question

The sum of Sn of first 'n' even natural numbers is given by the relation Sn =n(n+1) . Find n , if the sum is 420 ?

Answer 1

As Given:

(Let suffix "n" be suffix "a" also  values of n = a)

Sₐ = a(a+1)


To Find:

Value of n, if the sum is 420


Solution:

Sₐ = a(a+1)

420 = a(a+1)

420 = a² + a

= a² + a - 420

= a² + 21a - 20a -420

(splitting middle term)

= a(a+21) - 20(a+21)

=(a-20)(a+21)

Then,

"a" would be 20,-21

Negative Neglected as Natural no/s cannot be negative and also -21 is

not an even no


Hence value of a = n = 20 terms


Answer: n = 20 

☺ Hope this Helps ☺