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Consider a geometric sequence who third term is 9 and whose sixth term is -8/3. What is the first term? QUICKLY PLEASE!

Respuesta :

mhanifa

Answer:

  • 81/4

Step-by-step explanation:

Given

Geometric sequence with:

  • a₃ = 9
  • a₆ = -8/3

To find

  • The first term a₁

Solution

Formula for nth term is:

  • aₙ = a₁rⁿ⁻¹

For the given terms we have:

  • a₃ = a₁r² and
  • a₆ = a₁r⁵

Comparing the terms:

  • a₆/a₃ = r³

Substituting values to find the value of r:

  • -8/3 : 9 = -8/27 = (-2/3)³
  • r³ = (-2/3)³
  • r = -2/3

Then finding a₁:

  • a₁(-2/3)² = 9
  • a₁(4/9) = 9
  • a₁ = 81/4

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