contestada

The first term of a geometric sequence is 8 and the fourth term is 216. what is the sum of the first 12 terms of the corresponding series?

Respuesta :

The sum of the 12 terms of a geometric sequence with first term as 8 and fourth term as 216 is 2125760

Geometric sequence

The formula to solve geoemtric sequence is as follows:

aₙ = arⁿ⁻¹

where

  • a = first term
  • n = number of terms
  • r = common ratio

Therefore,

ar³ = 216

a = 8

Hence,

8r³ = 216

r³ = 216 / 8

r³ = 27

r = ∛27

r = 3

Therefore,

sum of 12 term = a(rⁿ - 1) / r - 1

S₁₂ = 8(3¹² - 1) / 3 - 1

S₁₂ = 8(531440)  / 2

S₁₂ = 4251520 / 2

S₁₂ = 2125760

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