Quadratic sequence has x;4;8;4;8;y determine the value of x and y if it second difference is 4
sorry. There's no way a quadratic sequence can go up, down, up, if the 2nd difference is constant.
To find the values of x and y in the quadratic sequence, we need to analyze the pattern of the given sequence. The second difference is the difference between consecutive terms in the first difference, and it helps us identify the pattern.
Let's look at the given sequence step by step:
1. The sequence starts with x, and the first term after x is 4. The common difference between these two terms is 4 - x.
2. The next term is 8. Since the first difference is the same for all consecutive terms, the common difference between 4 and 8 is also 4.
3. The term after 8 is 4. Again, the common difference remains 4.
4. Finally, we have the term y. Continuing with the pattern, the common difference between 4 and y is also 4.
Based on the given information, we can see that the common difference throughout the sequence is 4. Now, let's determine the values of x and y.
Given that the common difference is 4, we can find the missing terms by adding 4 to the previous term. Let's follow this process:
x + 4 = 4 -> x = 4 - 4 -> x = 0
8 + 4 = 12 -> y = 8 + 4 -> y = 12
Therefore, the value of x is 0 and the value of y is 12.
To solve this problem, let's first try to understand the given quadratic sequence:
The sequence is x, 4, 8, 4, 8, y.
We can see that the sequence alternates between two numbers: 4 and 8.
Now, let's analyze the differences between consecutive terms:
The difference between the first and second terms is 4 - x.
The difference between the second and third terms is 8 - 4 = 4.
The difference between the third and fourth terms is 4 - 8 = -4.
The difference between the fourth and fifth terms is 8 - 4 = 4.
The difference between the fifth and sixth terms is y - 8.
We are given that the second difference is 4. This means that the differences between consecutive differences are constant.
The differences between consecutive differences are:
4 - x, 4, -8, 4, y -8.
Since the second difference is 4, we have:
4 - x = 4
Solving this equation, we find:
x = 0
Now, to find the value of y, let's look at the differences between consecutive differences again:
4 - x, 4, -8, 4, y - 8.
Since the third difference is constant and equals -8, we have:
-8 = y - 8
Solving this equation for y, we find:
y = 0
Therefore, the value of x is 0 and the value of y is also 0. The quadratic sequence is 0, 4, 8, 4, 8, 0.