Question

The sum of the first six terms of ap,✓2,√8,√18,.........Is....

Answer 1

Given AP is ✓2,√8,√18,........

that is ✓2, 2✓2, 3✓2, ........

Here first term a = ✓2 and common difference d = 2✓2- ✓2 = ✓2

So sum of first six terms is

S₆ = 6/2 [2(✓2)+(6-1)✓2]         [ usin Sn = n/2 [2a+(n-1)d] ]

⇒ S₆ = 3[2✓2+5✓2]

⇒ S₆ = 3(7✓2)

⇒ S₆ = 21√2