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.
-2, -8, -32
find the next two terms of this sequence.
give exact values (not decimal approximations).
-2, -8, -32, ,

Explanation:

Step1: Find the common ratio

In a geometric sequence, the common ratio \( r \) is found by dividing a term by its previous term. Let's take the second term and divide by the first term: \( r=\frac{-8}{-2} = 4 \). We can check with the third term and the second term: \( \frac{-32}{-8}=4 \), so the common ratio \( r = 4 \).

Step2: Find the fourth term

To find the next term (fourth term) in a geometric sequence, we multiply the third term by the common ratio. The third term is \( -32 \), so the fourth term is \( -32\times4=-128 \).

Step3: Find the fifth term

To find the fifth term, we multiply the fourth term by the common ratio. The fourth term is \( -128 \), so the fifth term is \( -128\times4 = -512 \).

Answer:

-128, -512