[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522697-105":59,"doc-detail-522697-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","introduction-to-sequences","Introduction to Sequences","","Worksheet for practicing sequences in Infinite Algebra 2, focusing on finding missing terms and identifying patterns. Tasks include determining the next three terms, calculating the tenth term, and writing the first four terms for multiple given sequences. Students also write explicit and recursive formulas that generate the sequences, reinforcing recognition of arithmetic, geometric, and other rule-based term progressions. Includes several worked answer blanks to complete.",{"@graph":69,"@context":122},[70,84,105],{"@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/introduction-to-sequences/522697/",{"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/introduction-to-sequences/522697.png","ImageObject",300,407,{"name":92,"@type":93},"\tJames","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What kinds of problems are included on the worksheet?","Question",{"text":112,"@type":113},"It includes finding the next three terms, finding the tenth term, and finding the first four terms of given sequences, plus writing explicit and recursive formulas.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does “explicit formula” mean in these sequence problems?",{"text":117,"@type":113},"An explicit formula gives a direct expression for the nth term, allowing you to compute any term without using earlier terms.",{"name":119,"@type":110,"acceptedAnswer":120},"How are recursive formulas different from explicit formulas?",{"text":121,"@type":113},"A recursive formula defines the sequence using earlier terms (and parameters like a1 or a previous term), so the next term depends on a prior value.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522697,1791732245,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},2336474466412,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Algebra 2 Name   \nIntroduction to Sequences Date  Period   \nFind the next three terms in each sequence.  \n1) 1, −3, 9, −27, 81, ... 2) 9, 109, 209, 309, 409, ...  \n3) 0, 3, 8, 15, 24, ...  1   1   3   1   5   \n4) , , , , , ...  \n2 2 8 4 32  \n5) 4, 16, 36, 64, 100, ... 6) 14, 34, 54, 74, 94, ...  \n5   5   5   5  8) −9, 101, −999, 10001, −99999, ...  \n7) 5, , , , , ...  \n2 4 8 16  \nFind the tenth term in each sequence.  \n2   7   17  10) 7 9 12 16 21  \n9) −1, , , 4, , ... , , , , , ...  \n3 3 3  \n11) −2, −6, −18, −54, −162, ... 12) −23, −18, −13, −8, −3, ...  \n13) −4, 12, −36, 108, −324, ...  3  \n14) −6, −2, 0, 1, , ...  \n2  \n15) −28, 172, 372, 572, 772, ... 16) 37, 46, 55, 64, 73, ...  \nFind the first four terms in each sequence.  \n2n + 1  18) a = 3 n − 1  \n17) an = 3 n  \nn  \n19) a = n 2 + 1 n 3  \nn 20) a = ~~ ~~  \nn 2n + 1  \nFind the tenth term in each sequence.  \n21) an = ~~ ~~2nn+3~~ ~~1~~ ~~ 22) an = 4n − 1  \n23) a = (2n)2 24) a = (2n − 1)2 n n  \nFind the first four terms in each sequence.  \n25) an = an − 1 + 10 26) an = an − 1 ⋅ 2 a 1 = 29 a 1 = −1  \n27) an = an − 1 + n  2 + an − 1 a 1 = −4 28) an = 2  \na 1 = 10  \nFind the tenth term in each sequence.  \n29) an = nan − 1 30) an = an − 1 + 10 a 1 = −1 a 1 = 11  \n31) an = an − 1 ⋅ 3  2 + an − 1 a 1 = −3 32) an = 2  \na 1 = −14  \nWrite the explicit formula for each sequence.  \n33) −12, −9, −6, −3, 0, ...  3   6  \n34) −6, −3, −2, − , − , ...  \n2 5  \nWrite the recursive formula for each sequence.  \n35) 2, 4, 7, 11, 16, ... 36) 15, 215, 415, 615, 815, ...  \nKuta Software-Infinite Algebra 2  \nIntroduction to Sequences  \nFind the next three terms in each sequence.  \n1) 1, −3, 9, −27, 81, ...  \n−243, 729, −2187  \n3) 0, 3, 8, 15, 24, ...  \n35, 48, 63  \nName___________________________________  \nDate________________ Period____  \n2) 9, 109, 209, 309, 409, ...  \n509, 609, 709  \n4) 12~~ ~~ , 12~~ ~~ , 38~~ ~~ , 14~~ ~~ , 532~~ ~~ , ...  \n 3 , 7 , 1 ; Note: a = ~~ ~~n~~ ~~  \n32 128 32 n 2n  \n5) 4, 16, 36, 64, 100, ... 6) 14, 34, 54, 74, 94, ...  \n144, 196, 256 114, 134, 154  \n5   5   5   5  8) −9, 101, −999, 10001, −99999, ... 7) 5, , , , , ...  \n2 4 8 16  \n1000001, −9999999, 100000001  \n5 5 5  \n, ,  \n32 64 128  \nFind the tenth term in each sequence.  \n2   7   17  10) 7, 9, 12, 16, 21, ...  \n9) −1, , , 4, , ...  \n3 3 3 a 10 = 61 a 10 = 14  \n11) −2, −6, −18, −54, −162, ... 12) −23, −18, −13, −8, −3, ...  \na 10 = −39366 a 10 = 22  \n13) −4, 12, −36, 108, −324, ...  3  \n14) −6, −2, 0, 1,  \na 10 = 78732 2 , ...  \na 10 = ~~ ~~12764  \n15) −28, 172, 372, 572, 772, ... 16) 37, 46, 55, 64, 73, ...  \na 10 = 1772 a 10 = 118  \nFind the first four terms in each sequence.  \n17) an = ~~ ~~2nn+3~~ ~~1 3, 58~~ ~~ , 727~~ ~~ , 964~~ ~~ 18) an = 3 n − 1  \n1, 3, 9, 27  \n19) a = n 2 + 1 n 3 1 8 27 64  \nn 20) a = ~~ ~~ ~~ ~~ , ~~ ~~ , ~~ ~~ , ~~ ~~  \n2, 5, 10, 17 n 2n + 1 3 5 7 9  \nFind the tenth term in each sequence.  \n21) an = ~~ ~~2nn+3~~ ~~1~~ ~~ 22) an = 4n − 1  \na = 262144 10  \na 10 = ~~ ~~121000  \n23) a = (2n)2 24) a = (2n − 1)2 n n  \na 10 = 400 a 10 = 361  \nFind the first four terms in each sequence.  \n25) an = an − 1 + 10 a 1 = 29  \n29, 39, 49, 59  \n27) an = an − 1 + na 1 = −4  \n−4, −2, 1, 5  \nFind the tenth term in each sequence.  \n29) an = nan − 1  \na 1 = −1  \na 10 = −3628800  \n31) an = an − 1 ⋅ 3  \na 1 = −3  \na 10 = −59049  \nWrite the explicit formula for each sequence.  \n33) −12, −9, −6, −3, 0, ...  \na = −15 + 3n  \nn  \n26) an = an − 1 ⋅ 2 a 1 = −1  \n−1, −2, −4, −8  \n2 + a  \n28) a =  n − 1 n 2  \na 1 = 10  \n10, 6, 4, 3  \n30) an = an − 1 + 10 a 1 = 11  \na 10 = 101  \n32) a =  2 + an − 1  \nn 2  \na 1 = −14  \na 10 = ~~ ~~6332  \n34) −6, −3, −2, −  3  , −  6  , ... a = −  6  \n2 5 n n  \nWrite the recursive formula for each sequence.  \n35) 2, 4, 7, 11, 16, ...  \na = a + n  \nn n − 1  \na = 2  \n36) 15, 215, 415, 615, 815, ...  \na = a + 200  \nn n − 1  \na = 15  \n1 1  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com","cbCaid6d0Z0qispc","https://ap.wps.com/l/cbCaid6d0Z0qispc","pdf",36924,"English","# Find the next three terms in each sequence\n# Find the tenth term in each sequence\n# Find the first four terms in each sequence\n# Write the explicit formula for each sequence\n# Write the recursive formula for each sequence","[{\"question\":\"What kinds of problems are included on the worksheet?\",\"answer\":\"It includes finding the next three terms, finding the tenth term, and finding the first four terms of given sequences, plus writing explicit and recursive formulas.\"},{\"question\":\"What does “explicit formula” mean in these sequence problems?\",\"answer\":\"An explicit formula gives a direct expression for the nth term, allowing you to compute any term without using earlier terms.\"},{\"question\":\"How are recursive formulas different from explicit formulas?\",\"answer\":\"A recursive formula defines the sequence using earlier terms (and parameters like a1 or a previous term), so the next term depends on a prior value.\"}]","Introduction to Sequences | PDF",1791426069]