{(1,2),(3,4),(5,6),(7,8),(9,0)}
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We have a sequence that meets the given criteria, and with that information, we want to get the sum of all the terms in the sequence.
We will see that the sum tends to infinity.
So we have 5 terms;
A, B, C, D, E.
We know that the sum of each term and its neighboring terms is 15 or 25.
then:
- A + B + C = 15 or 25
- B + C + D = 15 or 25
- C + D + E = 15 or 25
Now, we want to find the sum of all the terms in the sequence (not only the 5 given).
Then let's assume we write the sum of infinite terms as:
Now we group that sum in pairs of 3 consecutive terms, so we get:
So we will have a sum of infinite of these, and each one of these is equal to 15 or 25 (both positive numbers). So when we sum that infinite times (even if we always have the smaller number, 15) the sum will tend to be infinite.
Then we have:
If you want to learn more, you can read:
Answer:
The equation is
Step-by-step explanation:
Let the quadratic function be
The point (-4,9) must satisfy this function,
The point (0,-7) must also satisfy this function,
The point (1,-1) must also satisfy this function,
We put equation 2 into equation 1 to get;
We again put equation 2 into equation 3 to get;
We add equation 5 and 6 to get;
We put into equation 6 to get;
The equation is therefore