I would recommend always try at least 2 terms, because you could always fluke one!įind the nth term of the quadratic sequence 1, 3, 9, 19, …įirst, find a – the difference of the differences divided by 2. It’s always a nice feeling, not just in maths, when you give an answer and you know it is correct. Let’s do the fourth term as well, we know this should be 12… N = 1 1 2 – 2×1 + 4 = 1 – 2 + 4 = 3 this matches our sequence! This allows us to check the formula we calculated is correct. that means the sequence is quadratic/power of 2. Likewise, we know that the second term in the sequence is 4, so if we plug 2 into the formula we should get 4. however, you might notice that the differences of the differences between the numbers are equal (5-32, 7-52). So, if we plug 1 into the formula we should get 3. We know from the question that the first term in the sequence is 3. You need to substitute the value of n into the formula. Going back to why the nth term formula is useful, remember that the formula tells you any term in the sequence. To work out terms in a quadratic sequence, you follow the same rules as you would for a linear sequence. What I would strongly recommend at this stage is that you check your answer. So the nth term of the green sequence is -2n + 4.Īdding this on to what we already knew, this means our nth term formula is n 2 – 2n + 4. The sequence has a difference of -2, and if there were a previous term it would be 4. If you need a reminder of how to find the nth term of a linear sequence, you can re-read the previous blog. We will need to add this on to n 2 – this will tell us our b and c. What we now need to do is find the nth term of this green sequence. This sequence should always be linear – if it isn’t, you have done something wrong. The differences between our sequence and the sequence n 2 now forms a linear sequence (in green above).
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