[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523574-105":59,"doc-detail-523574-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","geometric-sequences-and-series-kuta-software-infinite-precalculus-worksheet","Geometric Sequences and Series - Kuta Software Infinite Precalculus - Worksheet","","Worksheet for Infinite Precalculus practice on geometric sequences and geometric series. Tasks include identifying whether a sequence is geometric, determining the common ratio, finding a specified term such as the 8th term, and writing the explicit formula. It also covers converting between explicit and recursive forms, using two given terms to recover r and the formulas, filling in missing terms, evaluating finite geometric sums, finding the number of terms n, testing convergence or divergence, and evaluating infinite geometric series using the given conditions.",{"@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/geometric-sequences-and-series-kuta-software-infinite-precalculus-worksheet/523574/",{"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/geometric-sequences-and-series-kuta-software-infinite-precalculus-worksheet/523574.png","ImageObject",300,407,{"name":92,"@type":93},"pixelkiddo","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do I check whether a sequence is geometric?","Question",{"text":112,"@type":113},"Compute the ratio between consecutive terms and verify it is constant. If the ratio stays the same, the sequence is geometric; otherwise, it is not.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What information is needed to write the explicit and recursive formulas?",{"text":117,"@type":113},"You use the common ratio r and an initial term (often a1) to form the explicit formula. The recursive formula then expresses an+1 in terms of an using the same r.",{"name":119,"@type":110,"acceptedAnswer":120},"When does a geometric series converge or diverge?",{"text":121,"@type":113},"A geometric series converges only when the common ratio’s absolute value is less than 1. If |r| is greater than or equal to 1, it diverges.","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},523574,1791710843,{"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":44,"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},962090883892,"https://ap-avatar.wpscdn.com/avatar/e00115db34f3e0f11b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1790152879550218658","Kuta Software-Infinite Precalculus  \nGeometric Sequences and Series  \nName  Date  Period   \nDetermine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula.  \n1) 􀀐􀀔 , 􀀐􀀖 , 􀀐􀀜 , 􀀐􀀕􀀚 , ... 2) 􀀕 , 􀀔   􀀔   􀀔   \n􀀕 , 􀀛 , 􀀖􀀕 , ...  \n3) 􀀔􀀗􀀛 , 􀀔􀀗􀀛􀀛 , 􀀔􀀗􀀛􀀛􀀛 , 􀀔􀀗􀀛􀀛􀀛􀀛 , ... 4) 􀀓􀀑􀀚􀀘 , 􀀖 , 􀀔􀀕 , 􀀗􀀛 , ...  \nGiven the explicit formula for a geometric sequence find the common ratio, the term named in the problem, and the recursive formula.  \n5) an 􀀠 􀀐􀀖 􀂘 (~~ ~~􀀔􀀕~~ ~~) n 􀀐 􀀔 Find a 􀀔􀀔  \n6) an 􀀠 􀀐􀀔􀀑􀀘 􀂘 (􀀐􀀕)n 􀀐 􀀔 Find a 􀀔􀀓  \nGiven two terms in a geometric sequence find the common ratio, the explicit formula, and therecursive formula.  \n􀀔 8) a 􀀠 􀀐􀀕􀀗 and a 􀀠 􀀐􀀔􀀕  \n7) a􀀗 􀀠 􀀐  􀀗 and a 􀀔 􀀠 􀀕 􀀘 􀀗  \nFind the missing term or terms in each geometric sequence.  \n9) ..., 􀀗 , ___, ___, 􀀔􀀓􀀛 , ... 10) ..., 􀀐􀀕􀀘 ,   ,   ,   , 􀀐  􀀔   \n􀀕􀀘 , ...  \nEvaluate each geometric series described.  \n11) 􀀐􀀖 􀀎 􀀔􀀘 􀀐 􀀚􀀘 􀀎 􀀖􀀚􀀘 ..., n 􀀠 􀀛 12) 􀀕 􀀎 􀀛 􀀎 􀀖􀀕 􀀎 􀀔􀀕􀀛 ..., n 􀀠 􀀛  \n13) a 􀀔 􀀠 􀀔 , r 􀀠 􀀗 , n 􀀠 􀀚 14) a 􀀔 􀀠 􀀖 , r 􀀠 􀀕 , n 􀀠 􀀚  \n15) k􀀛 􀀔 􀀐􀀕 􀂘 􀀙 k 􀀐 􀀔 16) 􀀛􀀠 􀀔 􀀖􀀕 􀂘 (~~ ~~􀀔􀀕~~ ~~) m 􀀐 􀀔  \n􀀔􀀓 􀀔􀀓  \n17) 􀀶 􀀓􀀑􀀕 􀂘 􀀘 i 􀀐 􀀔 18) 􀀶 􀀐􀀕 􀂘 􀀕 n 􀀐 􀀔  \ni 􀀠 􀀔 n 􀀠 􀀔  \nDetermine the number of terms n in each geometric series.  \n19) 􀀶n 􀀐􀀗 i 􀀐 􀀔 􀀠 􀀐􀀖􀀗􀀔 20) a 􀀔 􀀠 􀀐􀀔 , r 􀀠 􀀐􀀘 , Sn 􀀠 􀀔􀀓􀀗  \ni 􀀠 􀀔  \nDetermine if each geometric series converges or diverges.  \n21) 􀀐􀀔 􀀎 􀀕 􀀐 􀀗 􀀎 􀀛 ... 22) 􀀐􀀔􀀙 􀀐 􀀗 􀀐 􀀔 􀀐 􀀔􀀗~~ ~~ ...  \n23) k 􀀐􀀖 􀂘 (~~ ~~􀀕􀀘~~ ~~)k 􀀐 􀀔 24) 􀀶i 􀁦􀀠 􀀔 􀀕 􀂘 􀀕 i 􀀐 􀀔  \nEvaluate each infinite geometric series described.  \n25) 􀀶i 􀁦􀀠 􀀔 (~~ ~~􀀔􀀖~~ ~~) i 􀀐 􀀔 26) 􀀶i 􀁦􀀠 􀀔 􀀓􀀑􀀗 􀂘 􀀓􀀑􀀜 i 􀀐 􀀔  \n27)  ( 􀀐 ~~ ~~􀀕􀀖~~ ~~) m 􀀐 􀀔 28) k 􀀐􀀗 k 􀀐 􀀔  \nKuta Software-Infinite Precalculus  \nGeometric Sequences and Series  \nName  Date  Period   \nDetermine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula.  \n1) 􀀐􀀔 , 􀀐􀀖 , 􀀐􀀜 , 􀀐􀀕􀀚 , ...  \nCommon Ratio: r 􀀠 􀀖 a􀀛 􀀠 􀀐􀀕􀀔􀀛􀀚 Explicit: an 􀀠 􀀐􀀖 n 􀀐 􀀔  \n3) 􀀔􀀗􀀛 , 􀀔􀀗􀀛􀀛 , 􀀔􀀗􀀛􀀛􀀛 , 􀀔􀀗􀀛􀀛􀀛􀀛 , ...  \nNot geometric  \n2) 􀀕 , 􀀔   􀀔   􀀔   \n􀀕 , 􀀛 , 􀀖􀀕 , ...  \n􀀔  \nCommon Ratio: r 􀀠 ~~ ~~􀀗  \n 􀀔  a􀀛 􀀠 􀀛􀀔􀀜􀀕  \nExplicit: an 􀀠 􀀕 􀂘 (~~ ~~􀀔􀀗~~ ~~) n 􀀐 􀀔  \n4) 􀀓􀀑􀀚􀀘 , 􀀖 , 􀀔􀀕 , 􀀗􀀛 , ...  \nCommon Ratio: r 􀀠 􀀗 a􀀛 􀀠 􀀔􀀕􀀕􀀛􀀛  \nExplicit: an 􀀠 􀀓􀀑􀀚􀀘 􀂘 􀀗 n 􀀐 􀀔  \nGiven the explicit formula for a geometric sequence find the common ratio, the term named in the problem, and the recursive formula.  \n5) an 􀀠 􀀐􀀖 􀂘 (~~ ~~􀀔􀀕~~ ~~) n 􀀐 􀀔 Find a 􀀔􀀔  \n􀀔  \nCommon Ratio: r 􀀠 ~~ ~~􀀕  \n 􀀖  a 􀀔􀀔 􀀠 􀀐 􀀔􀀓􀀕􀀗  \nRecursive: a 􀀠 an n 􀀐 􀀔 a 􀀔 􀀠 􀀐􀀖  \n 􀀔 􀂘  \n􀀕  \n6) an 􀀠 􀀐􀀔􀀑􀀘 􀂘 (􀀐􀀕)n 􀀐 􀀔 Find a 􀀔􀀓  \nCommon Ratio: r 􀀠 􀀐􀀕 a 􀀔􀀓 􀀠 􀀚􀀙􀀛  \nRecursive: an 􀀠 an 􀀐 􀀔 􀂘 􀀐􀀕 a 􀀔 􀀠 􀀐􀀔􀀑􀀘  \nGiven two terms in a geometric sequence find the common ratio, the explicit formula, and therecursive formula.  \n7)  \n 􀀔  a􀀗 􀀠 􀀐 􀀗  \nand a 􀀔 􀀠 􀀕 Common Ratio: r 􀀠 􀀐  􀀔   \nExplicit: an 􀀠 􀀕 􀂘 ( 􀀐 ~~ ~~􀀔􀀕~~ ~~) 􀀐 􀀔  \nRecursive: a 􀀠 an n 􀀐 􀀔  \n 􀀔 􀂘 􀀐  \n􀀕  \n8)  \na􀀘 􀀠 􀀐􀀕􀀗 and a􀀗 􀀠 􀀐􀀔􀀕  \nCommon Ratio: r 􀀠 􀀕  \nExplicit: an 􀀠 􀀐􀀔􀀑􀀘 􀂘 􀀕 n 􀀐 􀀔  \nRecursive: an 􀀠 an 􀀐 􀀔 􀂘 􀀕 a 􀀔 􀀠 􀀐􀀔􀀑􀀘  \na 􀀔 􀀠 􀀕  \nFind the missing term or terms in each geometric sequence.  \n9) ..., 􀀗 ,   ,   , 􀀔􀀓􀀛 , ... 􀀔  \n10) ..., 􀀐􀀕􀀘 ,   ,   ,   , 􀀐 ~~ ~~ , ...  \n􀀔􀀕 , 􀀖􀀙 􀀕􀀘  \n􀀐􀀘 , 􀀐􀀔 , 􀀐 ~~ ~~􀀔􀀘~~ ~~  \nEvaluate each geometric series described.  \n11) 􀀐􀀖 􀀎 􀀔􀀘 􀀐 􀀚􀀘 􀀎 􀀖􀀚􀀘 ..., n 􀀠 􀀛  \n􀀔􀀜􀀘􀀖􀀔􀀕  \n13) a 􀀔 􀀠 􀀔 , r 􀀠 􀀗 , n 􀀠 􀀚  \n􀀘􀀗􀀙􀀔  \n􀀛  \n15) 􀀶 􀀐􀀕 􀂘 􀀙 k 􀀐 􀀔  \nk 􀀠 􀀔  \n􀀐􀀙􀀚􀀔􀀛􀀗􀀙  \n􀀔􀀓  \n17) 􀀶 􀀓􀀑􀀕 􀂘 􀀘 i 􀀐 􀀔  \ni 􀀠 􀀔  \n􀀗􀀛􀀛􀀕􀀛􀀔􀀑􀀕  \n12) 􀀕 􀀎 􀀛 􀀎 􀀖􀀕 􀀎 􀀔􀀕􀀛 ..., n 􀀠 􀀛  \n􀀗􀀖􀀙􀀜􀀓  \n14) a 􀀔 􀀠 􀀖 , r 􀀠 􀀕 , n 􀀠 􀀚  \n􀀖􀀛􀀔  \n16) 􀀛􀀠 􀀔 􀀖 􀀕 􀂘 (~~ ~~􀀔􀀕~~ ~~) m 􀀐 􀀔  \n􀀕􀀘􀀘  \n􀀗  \n􀀔􀀓  \n18) 􀀶 􀀐􀀕 􀂘 􀀕 n 􀀐 􀀔  \nn 􀀠 􀀔  \n􀀐􀀕􀀓􀀗􀀙  \nDetermine the number of terms n in each geometric series.  \n19) 􀀶n 􀀐􀀗 i 􀀐 􀀔 􀀠 􀀐􀀖􀀗􀀔 20) a 􀀔 􀀠 􀀐􀀔 , r 􀀠 􀀐􀀘 ,  \ni 􀀠 􀀔 􀀗  \n􀀘  \nDetermine if each geometric series converges or diverges.  \nSn 􀀠 􀀔􀀓􀀗  \n21) 􀀐􀀔 􀀎 􀀕 􀀐 􀀗 􀀎 􀀛 ... 􀀔  \n22) 􀀐􀀔􀀙 􀀐 􀀗 􀀐 􀀔 􀀐 ~~ ~~ ...  \nDiverges 􀀗  \nConverges  \n23) k 􀀐􀀖 􀂘 (~~ ~~􀀕􀀘~~ ~~)k 􀀐 􀀔 24) 􀀶i 􀁦􀀠 􀀔 􀀕 􀂘 􀀕 i 􀀐 􀀔  \nConverges Diverges  \nEvaluate each infinite geometric series described.  \n25) 􀀶i 􀁦􀀠 􀀔 (~~ ~~􀀔􀀖~~ ~~) i 􀀐 􀀔 26) 􀀶i 􀁦􀀠 􀀔 􀀓􀀑􀀗 􀂘 􀀓􀀑􀀜 i 􀀐 􀀔  \n","cbCaiuykwzUakma8","https://ap.wps.com/l/cbCaiuykwzUakma8","pdf",30405,"English","# Determine Geometric Sequences\n## Identify geometric sequence, common ratio, 8th term, explicit formula\n# Convert and Use Formulas\n## From explicit to common ratio, named term, recursive formula\n## From two terms to common ratio, explicit formula, recursive formula\n# Missing Terms\n## Fill in missing terms in a geometric sequence\n# Evaluate Geometric Series\n## Evaluate each geometric series described (finite)\n## Determine the number of terms n\n# Convergence Tests\n## Determine if geometric series converges or diverges\n# Infinite Geometric Series\n## Evaluate each infinite geometric series described","[{\"question\":\"How do I check whether a sequence is geometric?\",\"answer\":\"Compute the ratio between consecutive terms and verify it is constant. If the ratio stays the same, the sequence is geometric; otherwise, it is not.\"},{\"question\":\"What information is needed to write the explicit and recursive formulas?\",\"answer\":\"You use the common ratio r and an initial term (often a1) to form the explicit formula. The recursive formula then expresses an+1 in terms of an using the same r.\"},{\"question\":\"When does a geometric series converge or diverge?\",\"answer\":\"A geometric series converges only when the common ratio’s absolute value is less than 1. If |r| is greater than or equal to 1, it diverges.\"}]","Geometric Sequences and Series - Kuta Software Infinite Precalculus - Worksheet | PDF",1791427041]