What is the formula for the following geometric sequence?

3, 12, 48, 192, ...

an = () · 3 n - 1

an = 4 · 3 n - 1

an = 3 · 4 n - 1

an = 3 · (-4) n - 1

Correct answer: a = 3 · 4⁽ⁿ ⁻ ¹⁾

Step-by-step explanation:

Given:

Geometric sequence 3, 12, 48, 192, ...

First term a₁ = 3

Second term a₂ = 12

Third term a₃ = 48

Common ratio or quotient:

q = a₂ / a₁ = a₃ / a₂ = 12 / 3 = 48 / 12 = 4

q = 4

First term a₁ = 3

Second term a₂ = a · q

Third term a₃ = a₂ · q = a₁ · q²

Fourth term a₄ = a₃ · q = a₁ · q³

...

n - th term aₙ = a₁ · q⁽ⁿ ⁻ ¹⁾

In this case aₙ = 3 · 4⁽ⁿ ⁻ ¹⁾

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