Question

$3, -6, 12, \dots$
enter the next two terms in the sequence in order separated by a comma.

identify the type of sequence.
○ arithmetic
○ geometric
○ neither arithmetic nor geometric
○ there is not enough information given

define an explicit function $f(n)$ for the sequence in terms of $n$. enter none if no

Explanation:

Step1: Find common ratio

$\frac{-6}{3} = -2$, $\frac{12}{-6} = -2$

Step2: Calculate 4th term

$12 \times (-2) = -24$

Step3: Calculate 5th term

$-24 \times (-2) = 48$

Step4: Identify sequence type

Common ratio is constant.

Answer:

Next two terms: $-24, 48$
Sequence type: Geometric