The first three terms of a geometric sequence are as follows.
4,20, 100
Find the next two terms of this sequence.
 


This is a geometric sequence, where each term is obtained by multiplying the previous term by a constant ratio, \( r \).

Given the first three terms are: 4, 20, and 100, we need to find the common ratio \( r \). The relationship between the terms can be expressed as:

\[
r = \frac{T_2}{T_1} = \frac{20}{4} = 5
\]
\[
r = \frac{T_3}{T_2} = \frac{100}{20} = 5
\]

Thus, the common ratio \( r \) is 5.

Now, to find the next two terms, we multiply the third term by the common ratio:

- \( T_4 = T_3 \times r = 100 \times 5 = 500 \)
- \( T_5 = T_4 \times r = 500 \times 5 = 2500 \)

The next two terms of the sequence are **500** and **2500**.

Would you like a detailed breakdown of how geometric sequences work, or do you have any further questions?

Here are five related questions to expand your understanding:
1. How do you find the sum of a geometric sequence?
2. What happens if the common ratio is a fraction?
3. How do you determine the nth term of a geometric sequence?
4. Can geometric sequences be used to model real-world growth or decay?
5. How do geometric series differ from arithmetic series?

**Tip:** In any geometric sequence, the common ratio can be positive, negative, or even a fraction. Always check by dividing consecutive terms!

The first three terms of a geometric sequence are as follows. 4, 20, 100. Find the next two terms of this sequence.

Learn how to find the next two terms in a geometric sequence starting with 4, 20, and 100. This problem demonstrates how to calculate the common ratio and apply it to extend the sequence, suitable for Grades 9-12.

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