[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-508190-105":59,"doc-detail-508190-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","arithmetic-sequences-as-linear-functions-section-45","Arithmetic Sequences as Linear Functions - Section 4.5","","Arithmetic Sequences as Linear Functions worksheet for PERT Math Section 4.5 focuses on connecting arithmetic sequences to linear functions. It provides quick review guidance on interpreting inputs and outputs, then offers practice problems covering finding next terms, common differences, recursive rules, missing terms, and identifying whether sequences are arithmetic. Word problems include growth in gym membership cost and expanding theater seat counts, with answer keys and step-by-step explanations.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/arithmetic-sequences-as-linear-functions-section-45/508190/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/arithmetic-sequences-as-linear-functions-section-45/508190.png","ImageObject",300,407,{"name":92,"@type":93},"Ophelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-05",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find a missing value in an arithmetic sequence?","Question",{"text":113,"@type":114},"Use the constant difference between consecutive terms. Then step forward or backward from a known term, or use the average formula for the middle of three terms.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is a recursive rule in this worksheet’s context?",{"text":118,"@type":114},"A recursive rule describes each term using the previous term. For example, the worksheet uses patterns like “each term equals the last one plus a fixed number.”",{"name":120,"@type":111,"acceptedAnswer":121},"How are arithmetic sequences used in the word problems?",{"text":122,"@type":114},"The scenarios translate into an initial value plus a constant monthly or row-based increase. The problems then ask for the cost after n months or the number of seats in a given row using the arithmetic sequence pattern.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},508190,1791527400,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":39,"preview_page_count":4},7971461741311,"https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826","Practice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nArithmetic Sequences as Linear Functions  \nPERT Math 􀀏 Section 4.5  \n\n| Name:   | D | ate:   | S | core:   / 12 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nA function pairs each input with exactly one output. Pay attention to what the input means, what rule is being applied, and whether the question asks for a value, a rule, a domain, or an interpretation.  \n▷ Example: For f(x) = 2x + 5, 􀀂nd f (4) .  \nWork: Replace x with 4: f (4) = 2(4) + 5 = 13 .  \n⋆ Answer: 13  \n♦ Practice Problems  \nSolve each problem. Show enough work that another student could follow your thinking.  \n1. Find the next three terms: 5 , 9 , 13 ,   6. Find a8 if a1 = 12 and d = 􀀀3 .  \n2. Find an for 7 , 10 , 13 ,   7. Write a recursive rule for 9 , 14 , 19 ,    \n3. Find the 12th term of 4 , 11 , 18 ,    \n8. Which term of 3 , 8 , 13 ,   is 48?  \n4. Is 2 , 6 , 12 , 20 ,   arithmetic?  \n9. Find an if a1 = 􀀀2 and d = 6 .  \n5. Find the common difference in 31 , 26 , 21 , 16 ,    \n10. Find the missing term: 4 , _ , 18 in an arithmetic sequence.  \n♦ Word Problems  \n11. A gym membership starts at $30 and adds $12 each month. Write the cost after n months.  \n12. A theater has 18 seats in row 1 and each row has 4 more seats. How many in row 9?  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n1.  17 , 21 , 25  7.  a1 = 9; an = an􀀀1 + 5   \n[2. ](2.  an = 3n)[ a](2.  an = 3n)[n](2.  an = 3n)[ = 3](2.  an = 3n)[n](2.  an = 3n) + 4  8. 10th  \n[3.](3. 81 9.  an = 6n)[ 81](3. 81 9.  an = 6n)[ 9. ](3. 81 9.  an = 6n)[ a](3. 81 9.  an = 6n)[n](3. 81 9.  an = 6n)[ = 6](3. 81 9.  an = 6n)[n](3. 81 9.  an = 6n) 􀀀 8   \n4. No 10. 11  \n5. 􀀀5 11. an = 12n + 18  \n6. 􀀀9 12. 50  \nStep-by-Step Explanations  \n1. Each term jumps up by 4, so just keep adding 4 to ride the pattern forward.  \n2. Start at 7, step by 3: 7 + 3(n 􀀀 1) tidies up into 3n + 4 .  \n3. From 4, you take 11 steps of 7 to reach term 12: 4 + 11(7) = 81 .  \n4. The gaps are 4 , 6 , 8—they keep growing, and arithmetic sequences need the same gap every time.  \n5. The terms are shrinking by 5 each step, so the difference is negative: 􀀀5 .  \n6. From the start, term 8 is 7 steps away: 12 + 7(􀀀3) drops you to 􀀀9 .  \n7. Recursive just means ’use the term before.’ Begin at 9, then each term is the last one plus 5.  \n8. Set 3 + 5(n 􀀀 1) = 48 . That gives 5(n 􀀀 1) = 45, so n = 10—the 10th spot holds 48.  \n9. Plug into the pattern: 􀀀2 + 6(n 􀀀 1) simpli􀀂es neatly to 6n 􀀀 8.  \n10. The middle of an arithmetic trio is just the average of its neighbors:(4 + 18)/2 = 11 .  \n11. Month 1 already costs 30, then 12 piles on each month: 30 + 12(n 􀀀 1) = 12n + 18 .  \n12. Row 9 is 8 rows past the 􀀂rst, gaining 4 seats","cbCaisKivkiqwuNx","https://ap.wps.com/l/cbCaisKivkiqwuNx","pdf",102361,"English","# Quick Review and Helpful Hints\n# Practice Problems\n## Word Problems\n# Answer Keys\n# Step-by-Step Explanations","[{\"question\":\"How do you find a missing value in an arithmetic sequence?\",\"answer\":\"Use the constant difference between consecutive terms. Then step forward or backward from a known term, or use the average formula for the middle of three terms.\"},{\"question\":\"What is a recursive rule in this worksheet’s context?\",\"answer\":\"A recursive rule describes each term using the previous term. For example, the worksheet uses patterns like “each term equals the last one plus a fixed number.”\"},{\"question\":\"How are arithmetic sequences used in the word problems?\",\"answer\":\"The scenarios translate into an initial value plus a constant monthly or row-based increase. The problems then ask for the cost after n months or the number of seats in a given row using the arithmetic sequence pattern.\"}]","Arithmetic Sequences as Linear Functions - Section 4.5 | PDF",1791212332]