Question

find the next two terms in this sequence.
64,32,16,8,4, ? ,

Explanation:

Step1: Identify the pattern

Looking at the sequence \(64, 32, 16, 8, 4\), we can see that each term is obtained by dividing the previous term by \(2\). Mathematically, if \(a_n\) is the \(n\)-th term, then \(a_{n + 1}=\frac{a_n}{2}\).

Step2: Find the 6th term

The 5th term is \(4\). To find the 6th term, we divide the 5th term by \(2\). So, \(a_6=\frac{4}{2} = 2\).

Step3: Find the 7th term

The 6th term is \(2\). To find the 7th term, we divide the 6th term by \(2\). So, \(a_7=\frac{2}{2}=1\).

Answer:

The next two terms are \(2\) and \(1\). So the sequence becomes \(64, 32, 16, 8, 4, \boldsymbol{2}, \boldsymbol{1}\).