Question

question 2 of 5

enter the correct answer in the box.

consider this geometric sequence:

(3, -12, 48, -192, \dots)

what is the explicit function that defines this sequence? (replace the (a) and (r) terms with the correct values.)

Explanation:

⚡ Using what you learned: Recursive and Explicit Formulas

Step 1: Identify the first term and common ratio

The given geometric sequence is:

$$ 3, -12, 48, -192, \dots $$

The first term \( a \) is:

$$ a = 3 $$

To find the common ratio \( r \), divide the second term by the first term:

$$ r = \frac{-12}{3} = -4 $$

Step 2: Write the explicit function

The explicit formula for a geometric sequence is given by:

$$ f(n) = a \cdot r^{n-1} $$

Substitute \( a = 3 \) and \( r = -4 \) into the formula:

$$ f(n) = 3 \cdot (-4)^{n-1} $$

Answer:

$$ f(n) = 3 \cdot (-4)^{n-1} $$