[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522593-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-522593-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","arithmetic-sequences-algebra-2-worksheet","Arithmetic Sequences - Algebra 2 Worksheet","","Arithmetic Sequences in Infinite Algebra 2 worksheet exercises determine whether given sequences are arithmetic and, when they are, compute the common difference. Students use explicit formulas an to find the first five terms and specific terms such as a34 and a39. Additional problems provide the first term and common difference to derive explicit and recursive forms, then find the next three terms after a specified last term. Some tasks also use two given terms to construct the recursive formula and identify subsequent terms.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/arithmetic-sequences-algebra-2-worksheet/522593/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/arithmetic-sequences-algebra-2-worksheet/522593.png","ImageObject",300,407,{"name":42,"@type":43},"Riley","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",8,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you tell whether a sequence is arithmetic?","Question",{"text":63,"@type":64},"Check whether the difference between consecutive terms is constant. If the common difference stays the same, the sequence is arithmetic.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What does the explicit formula an = ... help you find in these problems?",{"text":68,"@type":64},"It helps you compute the first five terms and the specific term named in the worksheet (for example, finding a34 or a39).",{"name":70,"@type":61,"acceptedAnswer":71},"How do you form the recursive formula from a first term a1 and common difference d?",{"text":72,"@type":64},"Use the rule an = a(n-1) + d (or an = a(n-1) - |d| depending on the sign of d) and start from the given a1, then generate the next terms.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522593,1791711250,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":123,"preview_page_count":4},1374391975076,"https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051","Kuta Software-Infinite Algebra 2 Name   \nArithmetic Sequences Date  Period   \nDetermine if the sequence is arithmetic. If it is, find the common difference.  \n1) 35, 32, 29, 26, ... 2) −3, −23, −43, −63, ...  \n3) −34, −64, −94, −124, ... 4) −30, −40, −50, −60, ...  \n5) −7, −9, −11, −13, ... 6) 9, 14, 19, 24, ...  \nGiven the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem.  \n7) an = −11 + 7n Find a34  \n9) an = −7.1 − 2.1n Find a27  \n8) an = 65 − 100n Find a39  \n10) an = ~~ ~~118 + ~~ ~~12n Find a23  \nGiven the first term and the common difference of an arithmetic sequence find the first five terms and the explicit formula.  \n11) a 1 = 28, d = 10 12) a 1 = −38, d = −100  \n13) a 1 = −34, d = −10 14) a 1 = 35, d = 4  \nGiven a term in an arithmetic sequence and the common difference find the first five terms and the explicit formula.  \n15) a38 = −53.2, d = −1.1 16) a40 = −1191, d = −30  \n17) a37 = 249, d = 8 18) a36 = −276, d = −7  \nGiven the first term and the common difference of an arithmetic sequence find the recursive formula and the three terms in the sequence after the last one given.  \n3   1  20) a = 39, d = −5  \n19) a 1 = , d = − 1 5 3  \n21) a 1 = −26, d = 200 22) a 1 = −9.2, d = 0.9  \nGiven a term in an arithmetic sequence and the common difference find the recursive formula and the three terms in the sequence after the last one given.  \n23) a21 = −1.4, d = 0.6 24) a22 = −44, d = −2  \n25) a 18 = 27.4, d = 1.1 26) a 12 = 28.6, d = 1.8  \nGiven two terms in an arithmetic sequence find the recursive formula.  \n27) a 18 = 3362 and a38 = 7362 28) a 18 = 44.3 and a33 = 84.8  \nKuta Software-Infinite Algebra 2 Name   \nArithmetic Sequences Date  Period   \nDetermine if the sequence is arithmetic. If it is, find the common difference.  \n1) 35, 32, 29, 26, ... 2) −3, −23, −43, −63, ...  \nd = −3 d = −20  \n3) −34, −64, −94, −124, ... 4) −30, −40, −50, −60, ...  \nd = −30 d = −10  \n5) −7, −9, −11, −13, ... 6) 9, 14, 19, 24, ...  \nd = −2 d = 5  \nGiven the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem.  \n7) an = −11 + 7n 8) an = 65 − 100n  \nFind a34 Find a39  \nFirst Five Terms: −4, 3, 10, 17, 24 First Five Terms: −35, −135, −235, −335, −435  \na34 = 227 a39 = −3835  \n9) an = −7.1 − 2.1n  11   1   15   19   23   27   31  \n10) a = + n First Five Terms:  \nFind a27 n 8 2 8 , 8 , 8 , 8 , 8  \nFind a 103  \nFirst Five Terms: −9.2, −11.3, −13.4, −15.5, −17.6 23 a23 =  8   \na = −63.8  \n27  \nGiven the first term and the common difference of an arithmetic sequence find the first five terms and the explicit formula.  \n11) a 1 = 28, d = 10 12) a 1 = −38, d = −100  \nFirst Five Terms: 28, 38, 48, 58, 68 First Five Terms: −38, −138, −238, −338, −438  \nExplicit: an = 18 + 10n Explicit: an = 62 − 100n  \n13) a 1 = −34, d = −10 14) a 1 = 35, d = 4  \nFirst Five Terms: −34, −44, −54, −64, −74 First Five Terms: 35, 39, 43, 47, 51  \nExplicit: an = −24 − 10n Explicit: an = 31 + 4n  \nGiven a term in an arithmetic sequence and the common difference find the first five terms and the explicit formula.  \n15) a38 = −53.2, d = −1.1 16) a40 = −1191, d = −30  \nFirst Five Terms: −12.5, −13.6, −14.7, −15.8, −16.9 First Five Terms: −21, −51, −81, −111, −141  \nExplicit: an = −11.4 − 1.1n Explicit: an = 9 − 30n  \n17) a37 = 249, d = 8  \nFirst Five Terms: −39, −31, −23, −15, −7  \nExplicit: an = −47 + 8n  \n18) a36 = −276, d = −7  \nFirst Five Terms: −31, −38, −45, −52, −59  \nExplicit: an = −24 − 7n  \nGiven the first term and the common difference of an arithmetic sequence find the recursive formula and the three terms in the sequence after the last one given.  \n19) a 1 = ~~ ~~35~~ ~~ , d = − ~~ ~~13 Next 3 terms: ~~ ~~415~~ ~~ , − ~~ ~~115~~ ~~ , − ~~ ~~25  \nRecursive: a = a −  1 n n − 1 3 a 1 = ~~ ~~35  \n21) a 1 = −26, d = 200  \nNext 3 terms: 174, 374, 574  \nRecursive: a = a + 200  \nn n − 1  \na 1 = −26  \n20) a 1 = 39, d = −5  \nNext 3 terms: 34, 29, 24  \nRecursive: a = a −","cbCaipX2NHQsvCqW","https://ap.wps.com/l/cbCaipX2NHQsvCqW","pdf",37998,"English","# Determine Arithmetic Sequences\n## Find Common Differences\n# Explicit Formulas: Find Terms\n## First Five Terms and Named Terms\n# Given a1 and d: Explicit and Recursive Forms\n## Next Three Terms\n# Given a Term and d: Recursive Formula and Next Terms\n# Given Two Terms: Recursive Formula","[{\"question\":\"How do you tell whether a sequence is arithmetic?\",\"answer\":\"Check whether the difference between consecutive terms is constant. If the common difference stays the same, the sequence is arithmetic.\"},{\"question\":\"What does the explicit formula an = ... help you find in these problems?\",\"answer\":\"It helps you compute the first five terms and the specific term named in the worksheet (for example, finding a34 or a39).\"},{\"question\":\"How do you form the recursive formula from a first term a1 and common difference d?\",\"answer\":\"Use the rule an = a(n-1) + d (or an = a(n-1) - |d| depending on the sign of d) and start from the given a1, then generate the next terms.\"}]","Arithmetic Sequences - Algebra 2 Worksheet | PDF",1791425953]