Respuesta :

mhanifa

Answer:

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)