Question

If sum of first n even natural numbers is 420 then the value of n s

Answer 1

Solution: We know that first even natural number is none other than 2 (two).

Sequence of A.P. = 2, 4, 6, 8.....

Given: 2 + 4 + 6 + 8...... = 420

→ Sn = n/2 × [2a + (n - 1)d]

→ 420 = n/2 × [2(2) + (n - 1)(2)]

→ 420 = n/2 × [4 + 2n - 2]

→ 840 = n[2 + 2n]

→ 0 = 2n² + 2n - 840

→ n = [- 2 ± √(2² - 4 × 2 × - 840)]/2(2)

→ n = [- 2 ± √(4 + 6720)]/4

→ n = [- 2 ± 82]/4

→ n = [- 2 - 82]/4 or [- 2 + 82]/4

→ n = - 21 or 20

Hence value of n is 20