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It includes tasks to write initial terms from explicit or recursive patterns, identify next apparent terms, and evaluate (when possible) limits of sequences. The practice also asks students to analyze convergence or divergence, compute limits, test for monotonicity and boundedness, and determine nth-term expressions. 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Write the next two apparent terms of the sequence: 2, 5, 8, 11,    \n\\#12 . Find the limit (if possible) of the sequence: a 􀀁  3n 􀀅1 n 5n 􀀂 2  \n\\#[9.](9. an)[ a](9. an)[n](9. an) 􀀁 􀀃􀀂1􀀄 n􀀅1 􀀆􀀈􀀊 ~~ ~~2n~~ ~~ 􀀇􀀋􀀉  \n􀀃 2n 􀀂1􀀄 !  \n\\#11 . Simplify: 􀀃 2n 􀀅1􀀄 !  \nDetermine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its  \nlimit:  \n\\# [13.](13. an)[ a](13. an)[n](13. an) 􀀁 ~~ ~~n~~ ~~5􀀅~~ ~~2  \n\\#15 . a 􀀁 􀀃 n 􀀅1􀀄 ! n n!  \n\\#17 . Determine whether the sequence is monotonic and whether it is bounded.  \nan 􀀁 4 􀀂 ~~ ~~1n  \n\\# [14.](14. an)[ a](14. an)[n](14. an) 􀀁 􀀃􀀂1􀀄 n􀀈􀀆􀀊 ~~ ~~n~~ ~~n􀀅~~ ~~1􀀇􀀋􀀉  \n\\#16 . a 􀀁  sin 􀀃 n 􀀄 n  \nn  \n\\#18 . Find an expression for the nth term:  \n1 2 3 4  \n􀀃 2 􀀄 􀀃 3􀀄 , 􀀃 3􀀄 􀀃 4 􀀄 , 􀀃 4 􀀄 􀀃 5􀀄 , 􀀃 5􀀄 􀀃 6 􀀄 , ...  \n7.2 – Required Practice  \nFind the sequence of partial sums S1, S2, S3, and S4.  \n1 1 1 1 9 27 81 243  \n\\#11 . 1 􀀅  􀀅  􀀅 ~~ ~~ 􀀅 ~~ ~~ 􀀅   \\#12 . 3 􀀂  􀀅 ~~ ~~ 􀀂 ~~ ~~ 􀀅 ~~ ~~ 􀀂    \n4 9 16 25 2 4 8 16  \nVerify that the infinite series diverges:  \n\\#13 . 0 5 􀀊􀀆􀀈 52~~ ~~ 􀀇􀀋􀀉 n \\#14 . 1 ~~ ~~nn22􀀅~~ ~~1  \nVerify that the infinite series converges:  \n\\#15 . 0 􀀆􀀊􀀈 56~~ ~~ 􀀇􀀋􀀉 n  \n\\#16 . 1 ~~ ~~n~~ 􀀃 ~~n1􀀅1~~􀀄~~  \n\\#17 . Find the sum of the convergent series \\#18 . Write the repeating decimal as a geometric And write the sum of the series as a fraction:  \n1 􀀂 􀀆􀀈􀀊 ~~ ~~15~~ ~~ 􀀇􀀋􀀉 n 0.81  \nDetermine if the series is convergent or divergent:  \n\\#19 . 0 ~~ ~~13n000  \n\\#20 .  ~~ ~~ln~~ ~~n~~ 􀀄~~  \n\\#21 .  e􀀂nn 􀀁 1  \n7.3 – Required Practice","cbCaicb4ts29hbdv","https://ap.wps.com/l/cbCaicb4ts29hbdv","pdf",410830,47,"English","# 7.1 - Required Practice\n## 7.1 problems on sequences and limits\n## 7.1 monotonicity, boundedness, and nth-term expressions\n# 7.2 - Required Practice\n## 7.2 partial sums and infinite series convergence/divergence\n## 7.2 sums of convergent series and geometric-series decimals","[{\"question\":\"What types of sequence questions are included in 7.1 Required Practice?\",\"answer\":\"7.1 includes writing the first terms of a sequence, finding the next terms from a pattern, and determining limits of sequences when possible.\"},{\"question\":\"How are convergence and divergence addressed in the required practice?\",\"answer\":\"In 7.2, the practice includes problems that require verifying whether infinite series diverge or converge, and finding sums when a series converges.\"},{\"question\":\"What additional properties of sequences are tested beyond limits?\",\"answer\":\"The practice asks students to determine whether a sequence is monotonic and whether it is bounded, using the given nth-term expression.\"}]","AP Calculus BC - Unit 7 Part 1 - Required Practice | PDF",1790736070,118]