Question

Question #35738

Answer 1

11640

Explanation:

Use the method of calculating formula of quadratic sequences.
Find the difference between numbers in the sequence and the difference of the difference too.

A template of the quadratic sequence is `an^2+bn+c`

So it is the law that the half of the difference of the difference should be `n`

The difference of differences is `-246` so `a=-123`
Find the differences between `-123n^2` and the sequence.

The differences of that will turn out to be unequal so find the differences of the differences.

The differences of differences between `-123n^2` and the sequence, which is `617`

Thus `b=617`

Substitute all the found values in the quadratic equation. But that would leave out the value `c`.

In order to find that make the equations, with substitutions already done, equal to the first element in the sequence. `n` would be the term in the sequence. In the first term `n` is `1` so its a variable.

`11634=617(1)-123(1)^2+c`

Make `c` the subject to get `c=11140`

The final sequence is `617n-123n^2+11140`

In the question, the first 3 are given, and we are looking for the next one which is the fourth one. So for this `n=4` would be the case.

When the values are substituted in the equation, it should equate to the next number in the sequence which is `11640`.

If the fact that the number is decreasing concerns you, it is because when a quadratic equation is graphed, it has a turning, so all the numbers after it are smaller.