Question

if the sum of the first n even natural number is 420 find the value of n

Answer 1

is that ten???
please answer

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

2 + 4 + 6 + 8 + ..... n = 420

Here,

Using Formula we have,

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

Situation,

⇒ n/2[2 × 2 + (n - 1) × 2] = 420

⇒ n(2 + n - 1) = 420

⇒ n(n + 1) = 420

⇒ n² + n = 420

⇒ n² + n - 420 = 0

Factorize it,

⇒ n² + n - 420 = 0

⇒ n² + 21n - 20n - 420 = 0

⇒ n(n + 21) - 20(n + 21) = 0

⇒ (n + 21)(n - 20) = 0

⇒ n + 21 = 0

⇒ n = -21 [Not Applicable]

Or

⇒ n - 20 = 0

⇒ n = 20

Therefore,

Value on n = 20