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Find the common ratio, the first five terms, and the explicit formula for the sequence aₙ = aₙ₋₁ * 3; a₁ = -3.

User LetsSyncUp
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Final answer:

The common ratio of the sequence is 3. The first five terms are -3, -9, -27, -81, and -243. The explicit formula for the sequence is an = -3 * 3n-1.

Step-by-step explanation:

The given sequence is defined by the formula an = an-1 * 3, with a1 = -3.

To find the common ratio of this sequence, we divide any term by its previous term. Let's divide the second term by the first term:

a2 / a1 = (a1 * 3) / a1 = 3.

So, the common ratio of this sequence is 3.

The first five terms of the sequence are:

  1. a1 = -3
  2. a2 = -3 * 3 = -9
  3. a3 = -9 * 3 = -27
  4. a4 = -27 * 3 = -81
  5. a5 = -81 * 3 = -243

The explicit formula for this sequence can be derived by recognizing that each term is obtained by multiplying the previous term by 3. Therefore, the explicit formula is an = a1 * 3n-1.

User Tony Borf
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