Question

Write an equation to describe the sequence

5/2, 5/4, 5/8

Answer 1

• aₙ = 5*2 ⁻ⁿ

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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