9/26/2023 0 Comments Quadratic sequences formula![]() ![]() 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… Isolate to solve for a,b and c and plug those values into the. N = 2 2 2 – 2×2 + 4 = 4 – 4 + 4 = 4 this also matches! Second common difference (2nd difference): the common difference of the common difference. 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. ![]() Likewise, we know that the second term in the sequence is 4, so if we plug 2 into the formula we should get 4. 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. Going back to why the nth term formula is useful, remember that the formula tells you any term in the 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. Use this to find out what numbers will continue in the sequence. 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). A quadratic sequence is given by Unan2+bn+c, where a,b and c are constants, n is the term and Un is the value of the term. ![]()
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