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!