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Exercises ask to determine whether given sequences are arithmetic, then compute the common difference, the 52nd term, the explicit formula, and the next three terms. Additional problems require converting an explicit formula into the common difference and recursive formula, using two given terms to derive explicit/recursive forms, finding missing terms, evaluating related sums and series, and determining the number of terms in each arithmetic series.",{"@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/arithmetic-sequences-and-series-kuta-software-infinite-precalculus-worksheets/523570/",{"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-and-series-kuta-software-infinite-precalculus-worksheets/523570.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":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you determine whether a sequence is arithmetic?","Question",{"text":112,"@type":113},"Compute the differences between consecutive terms and check whether they are constant. If the difference is consistent, the sequence is arithmetic and the common difference can be used for further questions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What formulas are requested for arithmetic sequences?",{"text":117,"@type":113},"Typical requests include the common difference d, a specific term (such as the 52nd term), the explicit formula an, and the recursive formula for an in terms of previous terms.",{"name":119,"@type":110,"acceptedAnswer":120},"How are arithmetic series problems evaluated in this worksheet?",{"text":121,"@type":113},"Given an arithmetic sequence description or explicit/term information, you evaluate the related series or arithmetic series by using the arithmetic-series structure to compute the requested sum or 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},523570,1791628611,{"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":52,"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  \nArithmetic Sequences and Series  \nName  Date  Period   \nDetermine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the explicit formula, and the three terms in the sequence after the last one given.  \n1) 􀀔􀀖 , 􀀔􀀘 , 􀀔􀀚 , 􀀔􀀜 , ... 2) 􀀗 , 􀀚 , 􀀔􀀕 , 􀀔􀀜 , ...  \n3) 􀀕 , 􀀘􀀕~~ ~~, 􀀖 , 􀀚􀀕~~ ~~ , ... 4) 􀀖􀀗 , 􀀕􀀛 , 􀀕􀀕 , 􀀔􀀙 , ...  \nGiven the explicit formula for an arithmetic sequence find the common difference, the term named in the problem, and the recursive formula.  \n5)  \nan 􀀠 􀀔􀀚 􀀎 􀀛 n Find a􀀖􀀜  \n6) an 􀀠 􀀐 ~~ ~~􀀘􀀕 􀀎 􀀖􀀕~~ ~~n Find a􀀕􀀕  \nGiven two terms in an arithmetic sequence find the common difference, the explicit formula, and the recursive formula.  \n7) a 􀀔􀀔 􀀠 􀀔􀀔􀀓 and a􀀖􀀚 􀀠 􀀖􀀚􀀓 8) a 􀀔􀀓 􀀠 􀀔􀀗 and a􀀖􀀚 􀀠 􀀔􀀕􀀕  \nFind the missing terms in each arithmetic sequence.  \n9) ..., 􀀖􀀕~~ ~~,   ,   , 􀀓 , ... 10) ..., 􀀖􀀑􀀗 , ___, ___, 􀀐􀀕 , ...  \nEvaluate the related series of each sequence.  \n11) 􀀖􀀑􀀚 , 􀀗􀀑􀀙 , 􀀘􀀑􀀘 , 􀀙􀀑􀀗 12) 􀀕􀀙 , 􀀖􀀙 , 􀀗􀀙 , 􀀘􀀙 , 􀀙􀀙 , 􀀚􀀙 , 􀀛􀀙  \nEvaluate each arithmetic series described.  \n13) a 􀀔 􀀠 􀀖􀀕~~ ~~ , d 􀀠 􀀔􀀕~~ ~~ , n 􀀠 􀀘􀀓 14) a 􀀔 􀀠 􀀐􀀕􀀕 , d 􀀠 􀀐􀀖 , n 􀀠 􀀔􀀕  \n15) a 􀀔 􀀠 􀀕􀀓 , an 􀀠 􀀘􀀘 , n 􀀠 􀀙 16) a 􀀔 􀀠 􀀔􀀗 , an 􀀠 􀀛􀀙 , n 􀀠 􀀔􀀓  \n17) 􀀔 􀀔 (􀀐􀀕 􀀎 􀀗􀀖~~ ~~m) 18) n􀀜 􀀔 (􀀚n 􀀐 􀀔􀀚)  \n19) 􀀖 􀀔 (􀀚m 􀀐 􀀔􀀕) 20) k􀀶􀀔 ( 􀀐 ~~ ~~􀀕􀀖 􀀎 􀀔􀀕~~ ~~k)  \n􀀔􀀓 􀀘􀀖  \n21) 􀀶 (􀀓􀀑􀀛i 􀀐 􀀙􀀑􀀖) 22) 􀀶 (􀀕n 􀀐 􀀚 )  \ni 􀀠 􀀕 n 􀀠 􀀗  \nDetermine the number of terms n in each arithmetic series.  \n23) 􀀔 􀀎 (􀀐􀀕) 􀀎 (􀀐􀀘 ) 􀀎 (􀀐􀀛) ..., Sn 􀀠 􀀐􀀕􀀘􀀜 24) 􀀔􀀛 􀀎 􀀕􀀔 􀀎 􀀕􀀗 􀀎 􀀕􀀚 ..., Sn 􀀠 􀀗􀀙􀀛  \nKuta Software-Infinite Precalculus  \nArithmetic Sequences and Series  \nName  Date  Period   \nDetermine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the explicit formula, and the three terms in the sequence after the last one given.  \n1) 􀀔􀀖 , 􀀔􀀘 , 􀀔􀀚 , 􀀔􀀜 , ...  \nCommon Difference: d 􀀠 􀀕  \nNext 3 terms: 􀀕􀀔 , 􀀕􀀖 , 􀀕􀀘 a􀀘􀀕 􀀠 􀀔􀀔􀀘  \nExplicit: an 􀀠 􀀔􀀔 􀀎 􀀕n  \n2) 􀀗 , 􀀚 , 􀀔􀀕 , 􀀔􀀜 , ...  \nNot arithmetic  \n3) 􀀕 , 􀀘􀀕~~ ~~, 􀀖 , 􀀚􀀕~~ ~~ , ... Common Difference: d 􀀠 􀀔􀀕  \n 􀀜   \nNext 3 terms: 􀀗 􀀘, 􀀕 ,  \n􀀘􀀘 a􀀘􀀕 􀀠  􀀕   \n 􀀖   􀀔  Explicit: an 􀀠 􀀕 􀀎 􀀕 n  \n4) 􀀖􀀗 , 􀀕􀀛 , 􀀕􀀕 , 􀀔􀀙 , ...  \nCommon Difference: d 􀀠 􀀐􀀙  \nNext 3 terms: 􀀔􀀓 , 􀀗 , 􀀐􀀕 a􀀘􀀕 􀀠 􀀐􀀕􀀚􀀕  \nExplicit: an 􀀠 􀀗􀀓 􀀐 􀀙n  \nGiven the explicit formula for an arithmetic sequence find the common difference, the term named in the problem, and the recursive formula.  \n5)  \nan 􀀠 􀀔􀀚 􀀎 􀀛 n Find a􀀖􀀜  \nCommon Difference: d 􀀠 􀀛 a􀀖􀀜 􀀠 􀀖􀀕􀀜  \nRecursive: an 􀀠 an 􀀐 􀀔 􀀎 􀀛 a 􀀔 􀀠 􀀕􀀘  \n6)  \n 􀀘   􀀖  a 􀀠 􀀐 􀀎 nn 􀀕 􀀕 Find a􀀕􀀕  \n􀀖  \nCommon Difference: d 􀀠 ~~ ~~  \n􀀕  \na􀀕􀀕 􀀠  \n 􀀙􀀔   \n􀀕  \nRecursive: a 􀀠 an n 􀀐 􀀔 a 􀀔 􀀠 􀀐􀀔  \n􀀎  \n 􀀖   \n􀀕  \nGiven two terms in an arithmetic sequence find the common difference, the explicit formula, and the recursive formula.  \n7) a 􀀔􀀔 􀀠 􀀔􀀔􀀓 and a􀀖􀀚 􀀠 􀀖􀀚􀀓  \nCommon Difference: d 􀀠 􀀔􀀓  \nExplicit: an 􀀠 􀀔􀀓n  \nRecursive: an 􀀠 an 􀀐 􀀔 􀀎 􀀔􀀓 a 􀀔 􀀠 􀀔􀀓  \n8) a 􀀔􀀓 􀀠 􀀔􀀗 and a􀀖􀀚 􀀠 􀀔􀀕􀀕  \nCommon Difference: d 􀀠 􀀗  \nExplicit: an 􀀠 􀀐􀀕􀀙 􀀎 􀀗n  \nRecursive: an 􀀠 an 􀀐 􀀔 􀀎 􀀗 a 􀀔 􀀠 􀀐􀀕􀀕  \nFind the missing terms in each arithmetic sequence.  \n9) ..., 􀀖􀀕~~ ~~,   ,   , 􀀓 , ... 􀀔 , 􀀔􀀕~~ ~~ 10) . . 􀀑,􀀙 ,􀀖􀀑􀀓, 􀀑 __, ___, 􀀐􀀕 , ...  \nEvaluate the related series of each sequence.  \n11) 􀀖􀀑􀀚 , 􀀗􀀑􀀙 , 􀀘􀀑􀀘 , 􀀙􀀑􀀗  \n􀀕􀀓􀀑􀀕  \nEvaluate each arithmetic series described.  \n13)  \na 􀀔 􀀠  \n 􀀖   \n􀀕 ,  \nd 􀀠 􀀔􀀕~~ ~~ , n 􀀠 􀀘􀀓  \n 􀀔􀀖􀀚􀀘   \n􀀕  \n15) a 􀀔 􀀠 􀀕􀀓 , an 􀀠 􀀘􀀘 , n 􀀠 􀀙  \n􀀕􀀕􀀘  \n17) 􀀔 􀀔 (􀀐􀀕 􀀎 􀀗􀀖~~ ~~m)  \n􀀔􀀙􀀓  \n􀀖  \n􀀖􀀘  \n19) 􀀶 (􀀚m 􀀐 􀀔􀀕)  \nm 􀀠 􀀔  \n􀀖􀀜􀀜􀀓  \n􀀔􀀓  \n21) 􀀶 (􀀓􀀑􀀛i 􀀐 􀀙􀀑􀀖)  \ni 􀀠 􀀕  \n􀀐􀀔􀀖􀀑􀀘  \n12) 􀀕􀀙 , 􀀖􀀙 , 􀀗􀀙 , 􀀘􀀙 , 􀀙􀀙 , 􀀚􀀙 , 􀀛􀀙  \n􀀖􀀜􀀕  \n14) a 􀀔 􀀠 􀀐􀀕􀀕 , d 􀀠 􀀐􀀖 , n 􀀠 􀀔􀀕  \n􀀐􀀗􀀙􀀕  \n16) a 􀀔 􀀠 􀀔􀀗 , an 􀀠 􀀛􀀙 , n 􀀠 􀀔􀀓  \n􀀘􀀓􀀓  \n􀀜  \n18) 􀀶 (􀀚n 􀀐 􀀔􀀚)  \nn 􀀠 􀀔  \n􀀔􀀙􀀕  \n20) k􀀶􀀔 ( 􀀐 ~~ ~~􀀕􀀖 􀀎 􀀔􀀕~~ ~~k)  \n􀀕􀀘􀀜  \n􀀙  \n􀀘􀀖  \n22) 􀀶 (􀀕n 􀀐 􀀚 )  \nn 􀀠 􀀗  \n􀀕􀀘􀀓􀀓  \nDetermine the number of terms n in each arithmetic series.  \n23) 􀀔 􀀎 (􀀐􀀕) 􀀎 (􀀐􀀘 ) 􀀎 (􀀐􀀛) ...,􀀔􀀗  \nSn 􀀠 􀀐􀀕􀀘􀀜 24) 􀀔􀀛 􀀎 􀀕􀀔 􀀎 􀀕􀀗 􀀎 􀀕􀀚 ..., Sn 􀀠 􀀗􀀙􀀛  \n􀀔􀀖  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaisFJglXPXoNr","https://ap.wps.com/l/cbCaisFJglXPXoNr","pdf",29458,"English","# Determine arithmetic sequences and next terms\n## Find common difference, 52nd term, and explicit formula\n# Convert between explicit and recursive forms\n## Problems using an explicit formula or two given terms\n# Missing terms and series evaluation\n## Evaluate related arithmetic series and arithmetic series\n# Determine number of terms n in arithmetic series","[{\"question\":\"How do you determine whether a sequence is arithmetic?\",\"answer\":\"Compute the differences between consecutive terms and check whether they are constant. If the difference is consistent, the sequence is arithmetic and the common difference can be used for further questions.\"},{\"question\":\"What formulas are requested for arithmetic sequences?\",\"answer\":\"Typical requests include the common difference d, a specific term (such as the 52nd term), the explicit formula an, and the recursive formula for an in terms of previous terms.\"},{\"question\":\"How are arithmetic series problems evaluated in this worksheet?\",\"answer\":\"Given an arithmetic sequence description or explicit/term information, you evaluate the related series or arithmetic series by using the arithmetic-series structure to compute the requested sum or value.\"}]","Arithmetic Sequences and Series - Kuta Software-Infinite Precalculus Worksheets | PDF",1791427035]