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ludmilkaskok [199]
3 years ago
7

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

Mathematics
1 answer:
kari74 [83]3 years ago
4 0

Answer:

  • 81/4

Step-by-step explanation:

<h3>Given</h3>

<u>Geometric sequence with:</u>

  • a₃ = 9
  • a₆ = -8/3
<h3>To find</h3>
  • The first term a₁
<h3>Solution</h3>

<u>Formula for nth term is:</u>

  • aₙ = a₁rⁿ⁻¹

<u>For the given terms we have:</u>

  • a₃ = a₁r² and
  • a₆ = a₁r⁵

<u>Comparing the terms:</u>

  • a₆/a₃ = r³

<u>Substituting values to find the value of r:</u>

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

<u>Then finding a₁:</u>

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