he\:first\:three\:terms\:of\:a\:geometric\:sequence\:are\:as\:follows.-5,\:10,\:-20\:\:Find\:the\:next\:two\:terms\:of\:this\:sequence.Give\:exact\:values\:\left(not\:decimal\:approximations\right).

The given terms of the geometric sequence are: -5, 10, -20.

In a geometric sequence, the ratio between consecutive terms is constant. Let the common ratio be \( r \).

To find the common ratio:
\[
r = \frac{\text{second term}}{\text{first term}} = \frac{10}{-5} = -2
\]
Now, let's verify this ratio with the third term:
\[
r = \frac{\text{third term}}{\text{second term}} = \frac{-20}{10} = -2
\]
So, the common ratio \( r = -2 \) is consistent.

To find the next two terms, we continue multiplying by \( r = -2 \).

The fourth term:
\[
\text{fourth term} = \text{third term} \times r = -20 \times (-2) = 40
\]

The fifth term:
\[
\text{fifth term} = \text{fourth term} \times r = 40 \times (-2) = -80
\]

Thus, the next two terms are:
\[
\boxed{40 \text{ and } -80}
\]

Would you like further explanation on this or have any questions?

Here are 5 related questions you might find useful:
1. What are the general properties of geometric sequences?
2. How do you determine the sum of a finite geometric sequence?
3. How can you find the general term of a geometric sequence?
4. What happens to a geometric sequence if the common ratio is a fraction?
5. How can you apply geometric sequences to real-world scenarios?

**Tip:** In any geometric sequence, if the common ratio \( r \) is negative, the terms will alternate in sign.

The first three terms of a geometric sequence are as follows: -5, 10, -20. Find the next two terms of this sequence. Give exact values (not decimal approximations).

Discover how to find the next two terms of the geometric sequence starting with -5, 10, and -20. This step-by-step solution involves calculating the common ratio and multiplying to find the fourth and fifth terms. Perfect for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation