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Write an equation to describe the sequence

5/2, 5/4, 5/8

1 Answer

3 votes

Answer:

  • aₙ = 5*2 ⁻ⁿ

-------------------

Given sequence:

  • 5/2, 5/4, 5/8, ...

We can see each term is half the previous one, hence it is a GP with:

  • a₁ = 5/4,
  • r = 1/2.

Its nth term is:

  • aₙ = a₁*rⁿ⁻¹
  • aₙ = 5/2*(1/2)ⁿ⁻¹ = 5/2 * 1/2ⁿ⁻¹ = 5 * 1/2ⁿ = 5*2 ⁻ⁿ

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