17 The sum of first 2 even natural numbers is given by the relationSn(

1.	17 The sum of first 2 even natural numbers is given by the relationSn(n +1). Find n if the sum is 420.
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 right answer

17 The sum of first 2 even natural numbers is given by the relationSn(n +1). Find n if the sum is 420.

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

right answer