How to find the nth term of a sequence...
Let's use the sequence 5, 9, 17, 29, 45 in our example. (This is a quadratic equation)
The general result form of our nth term should be an^2+bn+c.
The first difference is 4, 8, 12, and 16. Since these aren't the same, we need to find the second difference, which is 4, 4, and 4. It is the same, and there were two cycles of difference.
Divide 4(the result were got for the 2nd time) by 2(our number of cycles) to get N^2. This is the first part of our quest for the nth term!
Remember an^2+bn+c? The "a" part is 2 (4 divided by 2)
Draw an arrow on the first two numbers.
Remember this formula: 3a+b = difference between first two numbers of the original sequence. In this case, 4. (9-5)
So 3a+b=4. Remember that.
After some workings, we get b=-2
Now, to find the "c" part, have a+b+c=the first number(5)
After working, c=5
Plug in everything in the formula : 2n^2 – 2n + 5 and that's your Nth term.
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How to find the nth term of a quadratic sequence
RandomFinding the nth term of a quadratic sequence is difficult, or sometimes it is incomprehensible. So I hope to offer a somewhat simpler way to do this. It is a question most likely posed at GCSE students and A-level students who study mathematics.
