Question

The sum of first ..n' even natural numbers is 420 find the valie of n ❤️❤️answer plzz nest answer will get the brainliest ❤️✌️✌️​

Answer 1

Sum of first n even natural numbers is S=n(n-1)

Given Sum = 420

so, n(n-1) = 420

n²-n=420

n²-n-420=0

n²+21n-20n-420=0

n(n+21)-20(n+21)=0

(n-20)(n+21)=0

n=20 or n=-21

But here n is the number of first n natural numbers so n cannot be negative. So n=20

Answer 2

Answer:

Even natural no:s form an A.P :-

2,4,6,8 .....

a = 2 , d = 2 , Sn = 420

Sn = n/2 [ 2a + (n-1)d]

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

840 = n [ 2 + 2n ]

 2n²+ 2n = 840

2 [ n² + n ] = 840

n² + n = 420

n² + n - 420 = 0

               -------------

n = -b ± √ b² - 4ac  /   2a

     

   = -1 ± √1 - 4 x 1 x -420 = 2

 

    = -1 ± √1681 / 2

 

   = -1 ± 41 /2

 

   = -1 + 41/2 = 40/2 = 20

n = 20