given the quadratic sequence -2;0;3;7;...
2.1 write down the value of the next term of the sequence
1st difference: 2,3,4
2nd difference: 1,1,1
So, the 1st difference to the next term is 5, and the next term is 12
You just have to look for the pattern. you get 0 when you add -2 and 2, you get 3 when you add 0 and 3, and you get 7 when you add 3 and 4. There is a pattern; every time you make the next term, you raise the number by 1 to add to the previous number.
Since the gap between 3 and 7 was 4, the gap between 7 and the 5th term will be 5. 7+5=12
hope this helps!
Well, I'm not really a math whiz, but let me give it a shot! By looking at the sequence, it seems like the difference between consecutive terms increases by 1 each time. So, if we follow that pattern, the difference between 7 and the next term should be 4. Adding 4 to 7 gives us 11! So, my humorous answer would be: The value of the next term of the sequence is most likely 11, unless someone decides to throw in a curveball and make it something like an octopus. In that case, you might want to double-check with a real math expert just to be safe!
To find the value of the next term of the quadratic sequence -2, 0, 3, 7, ..., we need to first determine the pattern in the sequence.
To do this, let's find the differences between each consecutive term:
Difference between 0 and -2: -2 - 0 = -2
Difference between 3 and 0: 3 - 0 = 3
Difference between 7 and 3: 7 - 3 = 4
We notice that the difference between terms is not constant, indicating that the sequence is not linear. Let's check for a pattern in the differences:
Difference between 3 and 0: 3 - 0 = 3
Difference between 7 and 3: 7 - 3 = 4
Now, the differences between the differences are the same, indicating a quadratic pattern.
Let's find the difference between the differences:
Difference between 4 and 3: 4 - 3 = 1
Since the difference between the differences is constant, we can conclude that the original quadratic sequence has a quadratic formula of the form an^2 + bn + c.
To find the missing term, we continue the pattern by adding the next difference to the last term:
Last term (7) + Difference (1) = 8
Therefore, the value of the next term in the sequence is 8.
To find the value of the next term in the quadratic sequence -2; 0; 3; 7; ..., we first need to determine the pattern or rule of the sequence.
One way to do this is by examining the differences between consecutive terms. Let's calculate the differences:
0 - (-2) = 2
3 - 0 = 3
7 - 3 = 4
The differences between consecutive terms are increasing by one each time. This suggests that the sequence may have a quadratic relationship.
To determine the quadratic equation for the sequence, we need to find the second differences:
3 - 2 = 1
4 - 3 = 1
The second differences are constant, which indicates a quadratic relationship. Since the second differences are constant at 1, the quadratic equation is of the form an^2 + bn + c, where a = 1.
Now let's substitute the first few terms of the sequence into the quadratic equation to find the values of b and c:
For n = 1:
a(1)^2 + b(1) + c = -2
1 + b + c = -2
For n = 2:
a(2)^2 + b(2) + c = 0
4a + 2b + c = 0
Solving these two equations simultaneously, we find b = -1 and c = -3.
Therefore, the quadratic equation for the sequence is n^2 - n - 3.
To find the value of the next term (the 5th term) in the sequence, we substitute n = 5 into the quadratic equation:
(5)^2 - (5) - 3 = 25 - 5 - 3 = 17.
Therefore, the next term of the sequence is 17.