Question

the first three terms of a geometric sequence are as follows. 4, 20, 100 find the next two terms of this sequence. 4, 20, 100, \square, \square

Explanation:

Step1: Identify the common ratio

To find the common ratio \( r \) in a geometric sequence, we divide a term by its previous term. Let's take the second term and divide by the first term: \( r=\frac{20}{4} = 5 \). We can check with the third term and the second term: \( \frac{100}{20}=5 \). So the common ratio \( r = 5 \).

Step2: Find the fourth term

To find the fourth term, we multiply the third term (100) by the common ratio (5). So the fourth term is \( 100\times5 = 500 \).

Step3: Find the fifth term

To find the fifth term, we multiply the fourth term (500) by the common ratio (5). So the fifth term is \( 500\times5=2500 \).

Answer:

The next two terms are 500 and 2500.