Respuesta :

Answer:

-5015

Step-by-step explanation:

Sum of a Geometric Series (finite)

  • Sₙ = a(rⁿ - 1) / (r - 1)

Step 1 : Finding n

  • aₙ = -2560
  • r = -10/-5 = 2
  • a = -5
  • aₙ = arⁿ⁻¹
  • -2560 = -5(2)ⁿ⁻¹
  • 512 = (2)ⁿ⁻¹
  • 2⁸ = (2)ⁿ⁻¹
  • 8 = n - 1
  • n = 9

Step 2 : Substitute the values in the Sₙ formula

  • S₉ = -5(2⁹ - 1) / 2 - 1
  • S₉ = -5 x 1023
  • S₉ = -5015

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