Multiple choice

Identify the formula for the $n^{th}$ term of the sequence $54, 18, 6....$

  1. $54\left  (\dfrac{1}{3}\right)^{n-1}$
  2. $6 \left (\dfrac{1}{3}\right)^{n-1}$
  3. $3\left (\dfrac{1}{3}\right)^{n}$
  4. $54 \left (\dfrac{1}{3}\right)^{n}$
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A Correct answer
Explanation

This is a geometric progression with first term a = 54 and common ratio r = 18/54 = 1/3. The formula for the n-th term is a * r^(n-1), which is 54 * (1/3)^(n-1).

AI explanation

The sequence is a geometric progression with the first term 54 and a common ratio of 1/3. The formula for the nth term is a times r to the power of n minus 1. Therefore, the formula is 54 times 1/3 raised to the power of n minus 1.

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