11.2 and 11.3 Worksheets 2015.pdf, Study notes of Algebra

Download 11.2 and 11.3 Worksheets 2015.pdf and more Study notes Algebra in PDF only on Docsity! Pre-Calculus 11.2 Homework Name________________ [Day 2] Sequences & Series Worksheet [2015] Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. 1. 𝑎𝑛 = 8 + 13𝑛 2. 𝑎𝑛 = 1 𝑛+1 3. 𝑎𝑛 = 2𝑛 + 𝑛 Find the nth term of the sequence, then find the 20th term. 4. 𝑎1 = 2 and 𝑑 = 3 5. −6, −4, −2, …. 6. 𝑎1 = 0 and 𝑑 = 2 3 7. 2 5 , 1 15 , −4 15 , … Find the nth term of the sequence. 8. 𝑎1 = −4 and 𝑎5 = 16 9. 𝑎3 = 94 and 𝑎6 = 85 10. 𝑎5 = 190 and 𝑎10 = 115 Find the nth term of the sequence. 11. 𝑎6 = −38 and 𝑎11 = −73 12. 𝑎3 = 19 and 𝑎15 = −1.7 13. 𝑎5 = 16 and 𝑎14 = 38.5 Find the indicated nth partial sum (Sn) of the arithmetic sequence. 14. 8, 20, 32, 44, … 𝑛 = 10 15. 𝑎1 = −6, 𝑑 = 4, 𝑛 = 50 16. 100 + 105 + 110 + ⋯ + 220 17. 0.5 + 1.3 + 2.1 + … + 70.1 18. 𝑎1 = 3, 𝑑 = 2, 𝑛 = 12 19. 𝑎1 = 100, 𝑑 = −5, 𝑛 = 8 20. 𝑎2 = 8, 𝑎5 = 9.5, 𝑛 = 12 21. −3 + ( −3 2 ) + 0 + ⋯ + 30 Pre-Calculus 11.3 Homework Name________________ [Day 2] Sequences & Series Worksheet [2015] The nth term of a sequence is given. Find the first five terms of the sequence. 1. 𝑎𝑛 = 3(−4)𝑛−1 2. 𝑎𝑛 = 3𝑛−1 Find the nth term or the geometric sequence with giver first term a and a common ratio r. What is the fourth term? 3. 𝑎 = −6, 𝑟 = 3 4. 𝑎 = √3, 𝑟 = √3 Determine if the sequence is geometric. If it is geometric, find the common ratio. 5. 2, 6, 18, 36 … 6. 27, −9, 3, −1 … 7. 1 2 , 1 4 , 1 6 , 1 8 … Find the first five terms of the sequence and determine if it is geometric. If it is geometric, find the common ratio and express the nth term of the sequence in the standard form 𝒂𝒏 = 𝒂𝒓𝒏−𝟏 8. 𝑎𝑛 = 4 + 3𝑛 9. 𝑎𝑛 = (−1)𝑛2𝑛 10. 𝑎𝑛 = 𝑛𝑛 Determine the common ratio, the fifth term, and the nth term of the geometric sequence. 11. 7, 14 3 , 28 9 , 56 27 … 12. 1, √2, 2, 2√2 … 13. −8, −2, − 1 2 , − 1 8 … 14. The first term of a geometric sequence is 3, and the third term is 4 3 . Find the fifth term. 15. The common ratio in a geometric sequence is 3 2 , and the fifth term is 1. Find the first three terms. For the following problems, find the sum of the infinite geometric series, if possible. 16. 1 − 1 2 + 1 4 − 1 8 + ⋯ 17. 2 5 + 4 25 + 8 125 + ⋯ 18. 3 − 3 2 + 3 4 − 3 8 + ⋯ Express the repeating decimal as a fraction. 19. 0.253̅̅̅̅ 20. 0.123123123123 …