Subtracting 3n^2 from the sequence gives -3, -6, -9, -12, -15 which has nth term of -3n. Subtracting n^2 from the sequence gives 7, 10, 13, 15, 18, 21, and the nth term of this linear sequence is 3n + 4. Answer: The first differences are 11, 17, 23, and the second differences are 6. To find a, we find the difference of the differences in our sequence, and then divide this by 2. Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence. GCSE Revision Cards. Deduce expressions to calculate the nth term of quadratic and cubic sequences. Answer: First differences are 6, 8, 10, 12, 14, 16. Miss Achieve's maths tutorial on finding the nth term of linear and quadratic sequences. Answer: The first differences are 8, 10,12,14,16,18 and the second differences are 2. Answer: The first differences are 8,10,12,14,16,18 and the second differences are 2. Answer: The first differences are 14, 20, 26, 32, 38, and the second differences are 6. This means that the first term of the sequence is n^2. Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence. Now the nth term of these differences (4,8,12,16,20) is 4n. 6,20,40,66,98,136. Answer: The first difference of the sequence are 8, 10, 12, 24. Answer: The first differences are 14, 20, 26, 32 and 38, and so the second differences are all 6. When trying to find the nth term of a quadratic sequence, it will be of the form an 2 + bn + c where a, b, c always satisfy the following equations 2a = 2nd difference (always constant) 3a + b = 2nd term - 1st term a + b + c = 1st term Example: 1. Question: Find the nth term of this sequence 6, 12, 20, 30, 42, 56, 72? Step 1: Confirm the sequence is quadratic. Step 5: Write down your final answer in the form an² + bn + c. Step 1: Confirm if the sequence is quadratic. Subtracting n^2 from the sequence gives 7,12,17,22,27,32,37 which has a nth term of 5n + 2. So the nth term of this quadratic sequence is 3n^2 + 5n + 2. Consequently, the "difference between the differences between the sequence's terms is always the same".We say that the second difference is constant. Videos, worksheets, 5-a-day and much more a … Question: What is the nth term of 6, 20, 40, 66, 98,136? Search for: Contact us. Therefore, the formula for this sequence is 3n^2 -4n - 3. The calculator will generate all the work with detailed explanation. where does this difference came from, like the 4,8,12,16,20? Finding the nth term of quadratic sequences - Higher Quadratic sequences are sequences that include an \ (n^2\) term. Question: Find the nth term of 3,8,15,24? Half of 2 gives 1, so the first term of the nth term is n^2. The 4th term in the sequence is 33. So putting these two terms together gives n^2 + 3. Answer: The first differences are 0, 2, 4, 6, 8, 10 and the second differences are 2. So putting this together gives n^2 - 3n - 6. Quadratic nth Term Practice Questions Click here for Questions . Click to share on Twitter (Opens in new window), Click to share on Facebook (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to share on Pinterest (Opens in new window), GCSE Maths Revision: Finding the nth Term of a Quadratic Sequence, GCSE Maths Problem Solving Questions with Algebra, Revise My Last Duchess by Robert Browning: Power and Conflict Poems, Finding the nth Term of a Quadratic Sequence. Question: What is the nth term rule of the sequence -8, -8, -6, -2, 4? Subtracting n^2 from the sequence gives 2, 4, 6, 8 which has nth term of 2n. Therefore, the formula for this sequence is n^2 + 2n. Answer: The first differences are 8, 10, 12, 14, and the second differences are 2. If you want to see what we offer first, sign up for a free Twinkl account here and take a look around at our free resources. Question: What’s is the nth term of this: -4,1,12,29? Subtracting 3n^2 from the sequences gives 3,8,13,18,23 which has the nth term 5n-2. Look at the sequence: 3, 9, 19, 33, 51, …. Answer: The first differences are 3,7,11,15,19 and the second differences are 4. Hence, the logic of determining the terms of a given sequence defined by a quadratic formula should be the starting point. That’s £5 for as many resources as you can download with no limit! Question: What is the nth term of this: 3,18,41,72,111? Question: Find the nth term of this sequence 1,10,25,46,73,106? So the first difference between the terms in position 0 and 1 will be 6 − 4 = 2. we calculated the zeroth term as 1 and the 2nd difference as 4. where a is the 2nd difference ÷ 2 and c is the zeroth term, So far… in the sequence: 3, 9, 19, 33, 51, …. Question: Can you find the nth term of this quadratic sequence 4,7,12,19,28? They are different.] Since these are the same, this sequence is quadratic. So if you put the three-term together, this quadratic sequence has the nth term n^2 + 5n + 2. Quadratic nth Term Video 388 on www.corbettmaths.com Question 2: Below are patterns of tiles. 5-a-day Workbooks. A quadratic number sequence has nth term = an² + bn + c. Write down the nth term of this quadratic number sequence. Just put a decimal before n squared. Question: Find nth term of this sequence 10,33,64,103? Answer: The first differences are 7, 11, 15, 19. Question: Find the nth term of this sequence 4,13,28,49,76? GCSE Maths revision tutorial video.For the full list of videos and more revision resources visit www.mathsgenie.co.uk. Subtracting n^2 from the sequence gives 6,10,14,18,22,26, which has nth term of 4n + 2. Author: Jodi Bannister. 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