Question

the first three terms of a geometric sequence are as follows. 4, 12, 36 find the next two terms of this sequence. 4, 12, 36, \square, \square

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: \( r=\frac{12}{4} = 3 \). We can check with the third term and the second term: \( \frac{36}{12}=3 \). So the common ratio \( r = 3 \).

Step2: Find the fourth term

To find the next term (fourth term) in a geometric sequence, we multiply the last given term (third term, which is 36) by the common ratio \( r \). So, the fourth term \( a_4=a_3\times r=36\times3 = 108 \).

Step3: Find the fifth term

To find the fifth term, we multiply the fourth term (108) by the common ratio \( r \). So, the fifth term \( a_5=a_4\times r = 108\times3=324 \).

Answer:

The next two terms are 108 and 324.