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Students are asked to find the next terms, determine the first terms, and compute specific terms within sequences. The worksheet also requires rewriting series as sums and evaluating each series, along with rewriting expressions using sigma notation. Additional tasks ask students to judge whether sequences converge or diverge.",{"@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/sequences-and-series-infinite-precalculus-worksheet/523572/",{"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/sequences-and-series-infinite-precalculus-worksheet/523572.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":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What 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terms in each sequence.  \n1) 􀀔 , 􀀖 , 􀀙 , 􀀔􀀓 , 􀀔􀀘 , ... 2) 􀀐􀀗 , 􀀐􀀛 , 􀀐􀀔􀀙 , 􀀐􀀖􀀕 , 􀀐􀀙􀀗 , ...  \nFind the first four terms in each sequence.  \n3) an 􀀠 􀀖 􀂘 􀀗 n 􀀐 􀀔 4) an 􀀠 􀀐 ~~ ~~n~~ ~~~~ ~~􀀖~~ ~~  \n5) an 􀀠 an 􀀐 􀀔 􀂘 􀀐􀀘 6) an 􀀠 an 􀀐 􀀔 􀂘 􀀖 a 􀀔 􀀠 􀀓􀀑􀀗 a 􀀔 􀀠 􀀖  \nFind the tenth term in each sequence.  \n􀀔􀀘 8) a 􀀠 a 􀀎 n  \n7) an 􀀠 􀀐 ~~ ~~ n n 􀀐 􀀔  \nn a 􀀔 􀀠 􀀐􀀛  \nDetermine if each sequence converges or diverges.  \n9) 􀀐􀀖􀀓 , 􀀐􀀔􀀗 , 􀀐􀀙 , 􀀐􀀕 , 􀀓 , ... 10) 􀀛 , 􀀔􀀓􀀛 , 􀀕􀀓􀀛 , 􀀖􀀓􀀛 , 􀀗􀀓􀀛 , ...  \n11) an 􀀠 n~~ ~~~~ ~~􀀖~~ ~~ 12) an 􀀠 􀀐􀀗 􀂘 (􀀐􀀗)n 􀀐 􀀔  \n13) an 􀀠 an 􀀐 􀀔 􀂘 􀀕 􀀕 􀀎 an 􀀐 􀀔 a 􀀔 􀀠 􀀖 14) an 􀀠  􀀕   \na 􀀔 􀀠 􀀐􀀖􀀓  \nRewrite each series as a sum.  \n􀀗 􀀗  \n15) 􀀶 (􀀕􀀓 􀀐 n 􀀕 ) 16) 􀀶 (n 􀀎 􀀙􀀓􀀓)  \nn 􀀠 􀀔 n 􀀠 􀀔  \n􀀗 􀀔 􀀙 a 􀀕 􀀎 􀀔  \n17) 􀀶m 􀀠 􀀔 􀀖 m  18) a􀀶􀀠 􀀔 ~~ ~~a~~ ~~  \nEvaluate each series.  \n19) 􀀔􀀔􀀶 (m 􀀎 􀀗􀀓􀀓) 20) 􀀶􀀘  􀀔􀀓 m 􀀠 􀀘 n 􀀠 􀀔 n  \n21) 􀀶􀀙 􀀖􀀓􀀓  22) 􀀶􀀘 (􀀕􀀓 􀀐 n) k 􀀠 􀀔 k n 􀀠 􀀓  \n􀀘 􀀛  \n23) 􀀶 (􀀕􀀓􀀓 􀀐 k􀀕 ) 24) 􀀶 n  \nk 􀀠 􀀔 n 􀀠 􀀕  \n􀀜 􀀔 􀀚 a  \n25) n􀀶􀀠 􀀖 n~~ ~~ 26) a􀀶􀀠 􀀔 a 􀀎 􀀔   \nRewrite each series using sigma notation.  \n27) 􀀔 􀀎 􀀗 􀀎 􀀜 􀀎 􀀔􀀙 􀀎 􀀕􀀘 28) 􀀔 􀀎 􀀔􀀕~~ ~~ 􀀎 ~~ ~~􀀔􀀖~~ ~~ 􀀎 􀀔􀀗~~ ~~ 􀀎 ~~ ~~􀀔􀀘~~ ~~  \n29) 􀀔􀀖~~ ~~ 􀀎 ~~ ~~􀀔􀀜~~ ~~ 􀀎 􀀕􀀔􀀚~~ ~~ 􀀎 ~~ ~~􀀛􀀔􀀔~~ ~~ 􀀎 􀀕􀀔􀀗􀀖~~ ~~ 􀀎 ~~ ~~􀀚~~ ~~􀀔􀀕􀀜~~ ~~ 30) 􀀘 􀀎 􀀔􀀓 􀀎 􀀔􀀘 􀀎 􀀕􀀓 􀀎 􀀕􀀘  \n31) 􀀔􀀕~~ ~~ 􀀎 􀀕􀀖~~ ~~ 􀀎 􀀖􀀗~~ ~~ 􀀎 􀀗􀀘~~ ~~ 􀀎 ~~ ~~􀀘􀀙~~ ~~ 32) 􀀘 􀀎 􀀕􀀘 􀀎 􀀔􀀕􀀘 􀀎 􀀙􀀕􀀘 􀀎 􀀖􀀔􀀕􀀘  \nKuta Software-Infinite Precalculus Sequences and Series  \nFind the next three terms in each sequence.  \n1) 􀀔 , 􀀖 , 􀀙 , 􀀔􀀓 , 􀀔􀀘 , ...  \n􀀕􀀔 , 􀀕􀀛 , 􀀖􀀙  \nName  Date  Period   \n2) 􀀐􀀗 , 􀀐􀀛 , 􀀐􀀔􀀙 , 􀀐􀀖􀀕 , 􀀐􀀙􀀗 , ...  \n􀀐􀀔􀀕􀀛 , 􀀐􀀕􀀘􀀙 , 􀀐􀀘􀀔􀀕  \nFind the first four terms in each sequence.  \n3) an 􀀠 􀀖 􀂘 􀀗 n 􀀐 􀀔  \n􀀖 , 􀀔􀀕 , 􀀗􀀛 , 􀀔􀀜􀀕  \n5) an 􀀠 an 􀀐 􀀔 􀂘 􀀐􀀘 a 􀀔 􀀠 􀀓􀀑􀀗  \n􀀓􀀑􀀗 , 􀀐􀀕 , 􀀔􀀓 , 􀀐􀀘􀀓  \nFind the tenth term in each sequence.  \n7) an 􀀠 􀀐 ~~ ~~~~ ~~  \n 􀀖  a 􀀔􀀓 􀀠 􀀐 􀀕  \n4)  \n6)  \n8)  \n 􀀙  an 􀀠 􀀐 n 􀀎 􀀖  \n􀀐 ~~ ~~􀀖􀀕~~ ~~, 􀀐 ~~ ~~􀀙􀀘~~ ~~ , 􀀐􀀔 , 􀀐 ~~ ~~􀀙􀀚~~ ~~  \nan 􀀠 an 􀀐 􀀔 􀂘 􀀖 a 􀀔 􀀠 􀀖  \n􀀖 , 􀀜 , 􀀕􀀚 , 􀀛􀀔  \na 􀀠 a 􀀎 nn n 􀀐 􀀔 a 􀀔 􀀠 􀀐􀀛  \na 􀀔􀀓 􀀠 􀀗􀀙  \nDetermine if each sequence converges or diverges.  \n9) 􀀐􀀖􀀓 , 􀀐􀀔􀀗 , 􀀐􀀙 , 􀀐􀀕 , 􀀓 , ...  \nConverges  \n11)  \n13)  \na 􀀠  \nn  \n􀀙  \nn 􀀎 􀀖  \nConverges  \nan 􀀠 an 􀀐 􀀔 􀂘 􀀕 a 􀀔 􀀠 􀀖  \nDiverges  \n10) 􀀛 , 􀀔􀀓􀀛 , 􀀕􀀓􀀛 , 􀀖􀀓􀀛 , 􀀗􀀓􀀛 , ...  \nDiverges  \n12) an 􀀠 􀀐􀀗 􀂘 (􀀐􀀗)n 􀀐 􀀔  \nDiverges  \n14)  \n 􀀕 􀀎 an 􀀐 􀀔  an 􀀠 􀀕 a 􀀔 􀀠 􀀐􀀖􀀓  \nConverges  \nRewrite each series as a sum.  \n􀀗  \n15) 􀀶 (􀀕􀀓 􀀐 n 􀀕 )  \nn 􀀠 􀀔  \n􀀔􀀜 􀀎 􀀔􀀙 􀀎 􀀔􀀔 􀀎 􀀗  \n􀀗  \n17) 􀀶  \nm 􀀠 􀀔  \n􀀔  \n􀀖 m  \n 􀀔   􀀔   􀀔   􀀔   \n􀀎 􀀎 􀀎  \n􀀖 􀀜 􀀕􀀚 􀀛􀀔  \nEvaluate each series.  \n􀀔􀀔  \n19) 􀀶 (m 􀀎 􀀗􀀓􀀓)  \nm 􀀠 􀀘  \n􀀕􀀛􀀘􀀙  \n􀀙 􀀖􀀓􀀓  \n21) 􀀶 ~~ ~~  \nk 􀀠 􀀔 k  \n􀀚􀀖􀀘  \n􀀘  \n23) 􀀶 (􀀕􀀓􀀓 􀀐 k􀀕 )  \nk 􀀠 􀀔  \n􀀜􀀗􀀘  \n􀀜 􀀔  \n25) 􀀶 ~~ ~~  \nn 􀀠 􀀖 n  \n 􀀖􀀖􀀗􀀜 􀀕􀀘􀀕􀀓  \n􀀗  \n16) 􀀶 (n 􀀎 􀀙􀀓􀀓)  \nn 􀀠 􀀔  \n􀀙􀀓􀀔 􀀎 􀀙􀀓􀀕 􀀎 􀀙􀀓􀀖 􀀎 􀀙􀀓􀀗  \n􀀙 a 􀀕 􀀎 􀀔  \n18) 􀀶 ~~  ~~a 􀀠 􀀔 a  \n􀀕 􀀎 􀀘􀀕~~ ~~ 􀀎 ~~ ~~􀀔􀀓􀀖~~ ~~ 􀀎 ~~ ~~􀀔􀀚􀀗~~ ~~  \n􀀎  \n􀀕􀀙  \n􀀖􀀚  \n􀀘  \n􀀎  􀀙   \n􀀘 􀀔􀀓  \n20) 􀀶 ~~ ~~  \nn 􀀠 􀀔 n  \n 􀀔􀀖􀀚 􀀙  \n􀀘  \n22) 􀀶 (􀀕􀀓 􀀐 n)  \nn 􀀠 􀀓  \n􀀔􀀓􀀘  \n􀀛  \n24) 􀀶 n  \nn 􀀠 􀀕  \n􀀖􀀘  \n􀀚  \n26) a􀀶􀀠 􀀔 a~~ ~~a􀀎~~ ~~􀀔~~ ~~  \n 􀀔􀀗􀀚􀀜 􀀕􀀛􀀓  \nRewrite each series using sigma notation.  \n27) 􀀔 􀀎 􀀗 􀀎 􀀜 􀀎 􀀔􀀙 􀀎 􀀕􀀘  \n29) 􀀔􀀖~~ ~~ 􀀎 ~~ ~~􀀔􀀜~~ ~~ 􀀎 􀀕􀀔􀀚~~ ~~ 􀀎 ~~ ~~􀀛􀀔􀀔~~ ~~ 􀀎  \n31) 􀀔􀀕~~ ~~ 􀀎 􀀕􀀖~~ ~~ 􀀎 􀀖􀀗~~ ~~ 􀀎 􀀗􀀘~~ ~~ 􀀎 ~~ ~~􀀘􀀙~~ ~~  \n􀀘  \n􀀶 􀀕  \nm  \nm 􀀠 􀀔  \n􀀔  \n􀀕􀀗􀀖  \n􀀎  \n􀀔  \n􀀚􀀕􀀜  \n􀀘  \n􀀶 ~~ ~~a~~ ~~a 􀀠 􀀔 a 􀀎 􀀔  \n􀀙  \n􀀶  \nk 􀀠 􀀔  \n 􀀔   \n􀀖 k  \n􀀔 􀀔 􀀔 􀀔 􀀘 􀀔  \n28) 􀀔 􀀎 ~~ ~~ 􀀎 ~~ ~~ 􀀎 ~~ ~~ 􀀎 ~~ ~~ 􀀶 ~~ ~~  \n􀀕 􀀖 􀀗 􀀘 k 􀀠 􀀔 k  \n􀀘  \n30) 􀀘 􀀎 􀀔􀀓 􀀎 􀀔􀀘 􀀎 􀀕􀀓 􀀎 􀀕􀀘 􀀶 􀀘n  \nn 􀀠 􀀔  \n􀀘  \n32) 􀀘 􀀎 􀀕􀀘 􀀎 􀀔􀀕􀀘 􀀎 􀀙􀀕􀀘 􀀎 􀀖􀀔􀀕􀀘 􀀶 􀀘 a  \na 􀀠 􀀔  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaihMuizk2Ucqj","https://ap.wps.com/l/cbCaihMuizk2Ucqj","pdf",29064,"English","# Find the next three terms in each sequence\n# Find the first four terms in each sequence\n# Find the tenth term in each sequence\n# Determine if each sequence converges or diverges\n# Rewrite each series as a sum\n# Evaluate each series\n# Rewrite each series using sigma notation","[{\"question\":\"What kinds of questions appear in this worksheet?\",\"answer\":\"It includes tasks for next terms, first terms, and specific terms in sequences, plus convergence/divergence checks, series rewriting, evaluation, and sigma notation.\"},{\"question\":\"How are students supposed to handle the sequence convergence problems?\",\"answer\":\"Students must determine whether each sequence converges or diverges based on the given pattern and expression.\"},{\"question\":\"What does “rewrite each series using sigma notation” require?\",\"answer\":\"Students convert the given series into equivalent summation form using Σ notation with appropriate index limits and general term.\"}]","Sequences and Series - Infinite Precalculus worksheet | PDF",1791427038]