Half of 4 is 2, so the first term in the sequence is 2n^2. Calculate the term (n-ten) of sequence 2, 5, 10, 17, 26,. If you subtract 3n^2 from the sequence, you get 1 for each term. a, b and c come from the quadratic equation, which was written in its general form of There is no solution in the system of real numbers. You may be interested to know that the filling of the quadratic process to solve the quadratic equations on the equation ax 2 + bx + c = 0 was used to derive the quadratic formula. Calculate the first differences between the terms. The first differences are not the same, so calculate the second differences. Subtracting n^2 from the sequence gives you 7, 10, 13, 15, 18, 21, and the nth term of this linear sequence is 3n + 4. Following our previous blogs on identifying different types of sequences and searching for the nth term of a linear sequence, in this blog I will show you how to find the nth term of a square sequence. It is important to note that this topic can only be explored in the GCSE Higher Mathematics Exam. Let`s take an example. Now find the nth term of the green sequence. The sequence has a difference of 2 and if there was a previous term, it would be 5.So the nth term is 2n + 5.Give our final answer as n2 + 2n + 5.Check the first three terms.

n = 1 12 + 2×1 + 5 = 1 + 2 + 5 = 8 it corresponds to our sequences = 2 22 + 2×2 + 5 = 4 + 4 + 5 = 13 it also corresponds = 3 32 + 2×3 + 5 = 9 + 6 + 5 = 20 this is also consistent. This is not the simplest method, but with a little practice, you can learn it quite quickly. Try to find the nth term of these 5 square sequences. Put your answers in the comments or email your answers to sam@metatutor.co.uk and I`ll let you know if you`re doing them right. If you need someone to explain this to you personally, book a free trial lesson.1. 1, 7, 15, 25, . 2. 7, 12, 21, 34, . 3. 5, 12, 25, 44, . 4.

0, 9, 22, 39, . 5. 10, 19, 34, 55, . The second differences are the same. The sequence is square and contains a term (n^2). The coefficient of (n^2) is always half of the second difference. In this example, the second difference is 2. Half of 2 is 1, so the coefficient of (n^2) is 1. Therefore, the first term of the square sequence is n^2.

To calculate the (n)th term of the sequence, write the numbers in the sequence (n^2) and compare this sequence with the sequence of the question. The difference of differences this time is 4, so 4 ÷ 2 = 2, which gives us one = 2.So we know that our sequence begins with 2n2. Now compare our sequence with the sequence 2n2 (this is only the sequence for n2, but each term multiplied by 2). The differences between our sequence and the n2 sequence now form a linear sequence (green at the top). This sequence should always be linear – otherwise, you did something wrong. What we need to do now is find the nth term of this green sequence. We need to add this to n2 – it will tell us our b and c. If you want to remember how to find the nth term of a linear sequence, you can reread the previous blog. The sequence has a difference of -2, and if there was a previous term, it would be 4.So the nth term of the green sequence is -2n + 4. If you add this to what we already knew, it means that our nth term formula is n2 – 2n + 4. What I would highly recommend at this point is that you verify your answer.

Going back to why the nth term formula is useful, remember that the formula tells you each term in the sequence. We know from the question that the first term in order is 3. So if we put 1 in the formula, we should get 3. Similarly, we know that the second term in order is 4, so if we put 2 in the formula, we should get 4. In this way we can check if the formula we calculate is correct. And if we plug in 3, we should get 7.n = 1 12 – 2×1 + 4 = 1 – 2 + 4 = 3, which corresponds to our sequence!n = 2 22 – 2×2 + 4 = 4 – 4 + 4 = 4 which also suits !n = 3 32 – 2×3 + 4 = 9 – 6 + 4 = 7 which is also suitable! Let`s also do the fourth term, we know it should be 12. n = 4 42 – 2×4 + 4 = 16 – 8 + 4 = 12 4 of 4! We are therefore sure that our answer is correct. It`s always a nice feeling, not just in math, when you give an answer and know it`s right. I would always recommend trying at least 2 terms because you could always risk one! Example 2Find the nth term of the square sequence 1, 3, 9, 19, . First, find one – the difference in differences divided by the 2nd answer: It`s just the square sequence of numbers that doubles.

So, since half of 2 is 1, the first term is n^2. A third method of solving quadratic equations, which works with both real and imaginary roots, is called completing the square. Answer: These are the square numbers, with the exception of the first term of 1. A square with a missing term is called an incomplete square (as long as the axis-2 term is not missing). Answer: The first differences are 6,8,10,12,14. . .