AMC / AIME · Geometric Sequences · Hard

Geometric Sequences: math are consecutive positive geometric terms. Find math.

Common ratios.

Try the problem

x,12,27x,12,27 are consecutive positive geometric terms. Find xx.

Hint and answer

Concept to use

Infinite $|r|<1$.

Hint

Use ratios for terms and the finite or infinite geometric-sum formula.

Answer

16/3

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