What is the sum to 'n' terms of the series √5,√20,√45,√80,?

Sₙ = √5/2 n (n + 1)

Step-by-step explanation:

Given AP:

√5,√20,√45,√80,...

Rewriting as:

√5,√4*5,√9*5,√16*5,...√5, 2√5, 3√5, 4√5,..., n√5

Common difference:

d= 2√5 - √5 = √5

Sum of n terms:

Sₙ = 1/2n (a₁ + aₙ) =1/2n (√5 + √5 + (n-1)√5) =1/2n (n + 1)√5=√5/2 n (n + 1)

Sₙ = √5/2 n (n + 1)

Ithink the answer is b