9/11/2023 0 Comments Quadratic sequence 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. N = 4 4 2 – 2×4 + 4 = 16 – 8 + 4 = 12 4 out of 4! Nth term of a quadratic sequence with a proof at the end by Hannah Morris - April 19, 2020. Let’s do the fourth term as well, we know this should be 12… N = 3 3 2 – 2×3 + 4 = 9 – 6 + 4 = 7 this also matches! With solving quadratics, there can be an impulse to put everything in standard form and just use the quadratic formula. 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. A word with quad' in it usually implies four of something, like a quadrilateral. So, if we plug 1 into the formula we should get 3. The quadratic formula is an algebraic formula used to solve quadratic equations. 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. ![]() 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. They can be identified by the fact that the differences between the terms are not equal. You need to substitute the value of n into the formula. Quadratic sequences are sequences that include an n 2 term. We will need to add this on to n 2 – this will tell us our b and c. To work out terms in a quadratic sequence, you follow the same rules as you would for a linear sequence. 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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