Question

10.3 - geometric sequences
score: 9.5/24 answered: 10/24
question 10
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write a recursive formula for the sequence:
-6, 18, -54, 162, -486, ...
a₁ = -6, aₙ =

Explanation:

Step1: Identify the type of sequence

This is a geometric sequence, so we need to find the common ratio \( r \).
To find \( r \), divide a term by its previous term. For example, \( \frac{18}{-6} = -3 \), \( \frac{-54}{18} = -3 \), etc. So the common ratio \( r = -3 \).

Step2: Recall the recursive formula for a geometric sequence

The recursive formula for a geometric sequence is \( a_n = r \cdot a_{n - 1} \) with the initial term \( a_1 \).
We know \( a_1 = -6 \) and \( r = -3 \), so the recursive formula for \( a_n \) is \( a_n = -3 \cdot a_{n - 1} \) for \( n \geq 2 \).

Answer:

\( a_1 = -6 \), \( a_n = -3 \cdot a_{n - 1} \) (for \( n \geq 2 \))