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Find an explicit rule for each geometric sequence using subscript notation. Use a calculator and round your answers to the nearest tenth if necessary.

The fifth term of a geometric sequence is 7. The sixth term is 3.5.

Respuesta :

mhanifa

Answer:

  • aₙ = 224(1/2)ⁿ  

Step-by-step explanation:

Given GP with:

  • a₅ = 7
  • a₆ = 3.5

We can find the common ratio:

  • r = 3.5/7 = 1/2

Using the nth term formula we can work out the first term:

  • aₙ = a₁rⁿ⁻¹
  • a₅ = a₁(1/2)⁴
  • 7 = a₁ (1/16)
  • a₁ = 7*16
  • a₁ = 112

So the explicit rule is:

  • aₙ = 112(1/2)ⁿ⁻¹ = 224(1/2)ⁿ

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