Question

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

Answer 1

Sₙ = √5/2 n (n + 1)

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)