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How to Handle Quadratic Sequences

Updated: 6 days ago

There are several ways to find the equation for a quadratic sequence - I have found the following to be the best.


Quadratic sequences take the form:


If we substitute the first term (1) into the general form, we get…

Which simplifies to…

This is shown in the table below immediately beneath the term’s value.

Here we have a sequence of numbers. I have included the differences between the numbers in the sequence.

Notice that the 2nd difference is constant across the sequence- a sure sign that you have a quadratic sequence.


Finding the next number in the sequence is easy - add the 1st and second differences together from n=4 to n=5 (58 + 8 = 66) then add this to the value for n=5 (207 + 66 = 273). The value for n=6 is 273.


Let's find out the quadratic equation that gave this sequence of numbers...


From the derived equations in the first table, we can calculate the values for a, b and c.


Sequence = a + b + c = 23


1st difference = 3a + b = 34

2nd difference = 2a = 8