Consider the sequence that begins 40, 20, 10, 5,
Will the values of the sequence ever become zero or negative? Explain
no. You just keep multiplying by 1/2.
This was very helpful, so thank you
To determine if the values of the sequence will ever reach zero or become negative, we need to analyze the pattern and observe any trends.
From the given sequence, we can see that each term is obtained by dividing the previous term by 2. This pattern continues as follows:
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
Based on this pattern, we can conclude that each subsequent term will continue to be obtained by dividing the previous term by 2. This is because dividing a number by 2 results in a smaller value.
If we continue this pattern, we can predict the subsequent terms:
5 ÷ 2 = 2.5
2.5 ÷ 2 = 1.25
1.25 ÷ 2 = 0.625
0.625 ÷ 2 = 0.3125
As we can see, the values of the sequence approach but never quite reach zero. They continue to get smaller and closer to zero, but they will never become negative or actually reach zero.
Therefore, based on the pattern observed, the values of the given sequence will not become zero or negative.