Question

If the sum of first n even numbers is 420. Find the value of n.

Answer 1

ap-2,4,6,8,....
first term,a=2; common difference,d=2
we know sum of n terms=n/2(2a+(n-1)d)
therefore, 420=n/2(2*2+(n-1)2)
420=n/2(4+2n-2)
420=n/2(2+2n)
420=n+n2
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
therefore n=20(nth term can't be negative)
hence the value of n is 20(answer)
i hope it helps