![]() You can see that for this sequence, $2a=6$, $3a+b=11$ and $a+b+c=6$. In the table below you can see that the second difference is $2a$.Ĭomparing this new table to the original gives another way of figuring out the $n$th term. $3n^2+2n+1$īut why is the coefficient of $n^2$ half the second difference? Looking at the general case answers this question. The question marks in the table above can be replaced. Write down the $n$th term of this linear sequence. In this example the linear sequence is 3, 5, 7, … Subtract these numbers from the terms of the given sequence to obtain a linear sequence.Work out the first few terms of the sequence for which the $n$th term is $3n^2$.This is the coefficient of $n^2$ in the required $n$th term, because your teacher says so. ![]() The most popular method with teachers seems to be the following: There are several ways to find the $n$th term of a sequence. I hope that the pattern which allows you to work out the next term is clear. The second difference is found in a similar way. The first differences are found by selecting each term, after the first, and subtracting the previous term. In the table below the “working out” has been added below. If the first four terms of a quadratic sequence are 6, 17, 34, and 57, find the next term and the $n$th term. I’m going to focus on the second of these points.
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