Question

the first three terms of a geometric sequence are as follows. 32, 16, 8 find the next two terms of this sequence. 32, 16, 8, \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 \( 16 \) and divide it by the first term \( 32 \): \( r=\frac{16}{32}=\frac{1}{2} \). We can check with the third term: \( \frac{8}{16}=\frac{1}{2} \), so the common ratio \( r = \frac{1}{2} \).

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 \( 8 \)) by the common ratio \( r \). So, the fourth term \( a_4 = 8\times\frac{1}{2}=4 \).

Step3: Find the fifth term

To find the next term (fifth term) after the fourth term, we multiply the fourth term (\( 4 \)) by the common ratio \( r \). So, the fifth term \( a_5 = 4\times\frac{1}{2}=2 \).

Answer:

The next two terms are \( 4 \) and \( 2 \).