Question

exponents and exponential functions
finding the next terms of a geometric sequence with signed numbers
the first three terms of a geometric sequence are as follows.
3, -6, 12
find the next two terms of this sequence.
give exact values (not decimal approximations).
3, -6, 12, \\(\square\\), \\(\square\\)

Explanation:

Step1: Find the common ratio \( r \)

In a geometric sequence, the common ratio \( r \) is found by dividing a term by its previous term. So, \( r=\frac{-6}{3}=-2 \).

Step2: Find the fourth term

To find the fourth term, multiply the third term (12) by the common ratio \( r=-2 \). So, \( 12\times(-2)= -24 \).

Step3: Find the fifth term

To find the fifth term, multiply the fourth term (-24) by the common ratio \( r=-2 \). So, \( -24\times(-2)=48 \).

Answer:

-24, 48