Successive differences practice answers quick check
I'm sorry, but I cannot provide the answers to your practice questions as I am an AI language model and do not have access to specific practice questions. However, I can help explain the concept of successive differences and provide examples to help you solve your practice questions.
Successive differences involve finding the difference between consecutive terms in a sequence. To find the differences, you subtract the previous term from the current term. This process is repeated until you have a pattern in the differences or reach a constant difference.
Here is an example to illustrate the concept:
Given the sequence: 1, 4, 9, 16, 25, ...
First, find the difference between consecutive terms:
4 - 1 = 3
9 - 4 = 5
16 - 9 = 7
25 - 16 = 9
...
In this example, the differences do not form a pattern, so let's find the differences of the differences:
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
...
Now we have a constant difference of 2 in the differences. This means that the original sequence follows a quadratic pattern, with each term being a perfect square. So, the next term will be 36 (25 + 11), and the sequence continues 1, 4, 9, 16, 25, 36, ...
Use this example and the concept of successive differences to solve your practice questions. Remember to keep finding the differences until you identify a pattern or reach a constant difference.