[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-208560-en":3,"doc-seo-208560-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},208560,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",4,"Exam","11 Sequences - Worksheet 11","AQA Level 2 Further Mathematics worksheet focuses on sequence questions, combining linear and quadratic patterns. Students work on finding the first negative term, deriving nth terms, and using algebraic proofs to establish formulas such as n^2 + 3n and n^2 + 5n + 6. The worksheet also includes tasks with non-calculator constraints, parameter determination from given term values, and analysis of sequences involving differences, limiting values, and sequences formed from odd-number products.","|  | AQA Qualifications |  |\n| --- | --- | --- |\n|  |  |  |\n| AQA Level 2 Certificate\u003Cbr>FURTHER MATHEMATICS\u003Cbr>Level 2 (8360) |  |  |\n| Worksheet 11\u003Cbr>Sequences |  |  |\n\nOur specification is published on our website ([www.aqa.org.uk](www.aqa.org.uk) ) . We will let centres know in writing about any changes to the specification. We will also publish changes on our website. The definitive version of our specification will always be the one on our website, this may differ from printed versions.  \nYou can get further copies of this Teacher Resource from: The GCSE Mathematics Department  \nAQA  \nDevas Street Manchester M16 6EX  \nOr, you can download a copy from our All About Maths website ([http://allaboutmaths.aqa.org.uk/](http://allaboutmaths.aqa.org.uk/)) .  \nCopyright © 2012 AQA and its licensors. All rights reserved.  \nAQA retains the copyright on all its publications, including the specifications. However, registered centres for AQA are permitted to copy material from this specification booklet for their own internal use.  \nAQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (number 3644723) . Our registered address is AQA, Devas Street, Manchester M15 6EX.  \n11 Sequences  \nQuestion 1  \nA linear sequence starts  \n250 246 242 238    \nWhich term is the first to have a negative value? (4 marks)  \nQuestion 2  \nWork out the nth term of this quadratic sequence.  \n8 9 14 23 36    \n(4 marks)  \nQuestion 3  \n(a) Show that the nth term of the quadratic sequence  \n4 10 18 28   is n 2 + 3 n  \n(3 marks)  \n(b) Hence, write down the nth term of these quadratic sequences.  \n(b) (i) 5 11 19 29    \n(1 mark)  \n(b) (ii) 5 12 21 32    \n(1 mark)  \nQuestion 4 (non calculator)  \n(a) Write down the nth term of the linear sequence  \n4 7 10 13    \n(1 mark)  \n(b) Hence, write down the nth term of the quadratic sequence.  \n16 49 100 169    \n(1 mark)  \n(c) For the sequence in part 4(b), show that the 30th term is equal to the product  \nof the 2nd and 4th terms (3 marks)  \nQuestion 5  \n5 cm  \nThis pattern of rectangles continues.  \nShow that the sequence of numbers formed by the areas of these rectangles has nth term  \nn 2 + 5n + 6 (4 marks)  \nQuestion 6  \nA linear sequence starts  \na + b a + 3b a + 5b a + 7b    \nThe 5th and 8th terms have values 35 and 59.  \n(a) Work out a and b. (4 marks)  \n(b) Work out the nth term of the sequence. (2 marks)  \nLEVEL 2 CERTIFICATE FURTHER MATHEMATICS  \nQuestion 7  \nA sequence has nth term ~~ ~~3nn􀀎~~ ~~1  \n 1   \n(a) Show that the difference between the nth and (n + 1)th terms is (3 marks) n (n 􀀎 1)  \n(b) Which are the first two consecutive terms with a difference less than 0.01? (2 marks)  \n(c) Write down the limiting value of the sequence as n 􀀅 􀁦 (1 mark)  \nQuestion 8  \nA sequence has nth term ~~ ~~5n2􀀎n~~ ~~2  \nShow that the limiting value of the sequence, S, as n 􀀅 􀁦 is 2.5 (2 marks)  \nQuestion 9  \nHere is the sequence of odd numbers  \n1 3 5 7 9    \nA quadratic sequence is formed by multiplying consecutive odd numbers in successive pairs.  \n3 15 35 63    \nWork out the nth term of this sequence. (3 marks)  \nQuestion 10  \n2n2 􀀐 1  \nThe nth term of a sequence is ~~ ~~  \n3n2 􀀎 2  \n 3   \n(a) Show that the difference between the first two terms is (3 marks) 10  \n(b) Write down the limiting value of the sequence as n 􀀅 􀁦 (1 mark)","cbCaieIjIKo9WLWv","https://ap.wps.com/l/cbCaieIjIKo9WLWv","pdf",782416,1,5,"English","en",105,"# Question 1\n# Question 2\n# Question 3\n## (a) Prove the nth term\n## (b) Write down further nth terms\n# Question 4\n## (a) Linear nth term\n## (b) Quadratic nth term\n## (c) Show a product relationship\n# Question 5\n# Question 6\n# Question 7\n# Question 8\n# Question 9\n# Question 10","[{\"question\":\"How do you find the first negative term in a linear sequence?\",\"answer\":\"Determine the linear rule for the sequence and identify the smallest term index where the value becomes negative.\"},{\"question\":\"What is meant by the limiting value of a sequence in this worksheet?\",\"answer\":\"It is the value the sequence approaches as n grows large, found using the given nth-term expression.\"},{\"question\":\"How can a quadratic sequence be constructed from consecutive odd numbers?\",\"answer\":\"Multiply consecutive odd numbers in successive pairs, then derive the nth term of the resulting sequence from the pattern.\"}]","11 Sequences - 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