Describe a pattern in the sequence of numbers. Predict the next number.
256,16,4,2,...
It appears to me the next number is the square root of the preceeding number. What is the square root of 2?
Is it 4?
No. The square of 2 is 4. The square root of 2 MUST be smaller than 2. Pick up your calculator and take the square root of 2.
I got 1.414213561. Would it be 1.4?
It depends upon how many places you want to carry it. Since 256 has three places, I would carry the square root of 2 to 3 places and write 1.41.
To identify the pattern in the sequence, we need to look for a relationship or a rule that governs the behavior of the numbers. Let's analyze the given sequence:
256, 16, 4, 2
If we examine the sequence carefully, we can see that each number in the sequence is obtained by repeatedly dividing the previous number by 16. Specifically:
16 = 256 ÷ 16
4 = 16 ÷ 4
2 = 4 ÷ 2
Therefore, it seems that the pattern is to repeatedly divide the previous number by 16. Following this pattern, we can predict the next number in the sequence:
1 = 2 ÷ 2
Therefore, the next number in the given sequence is 1.