Math Arithmetic 11.2 Sequences and Series

Pre-Calculus 11.2 Homework Name________________ Date_________________ 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. 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 = Find the nth term of the sequence. 8. a1 = -4 and a5 = 16 9. a3 = 94 and a6 = 85 𝑛 𝑎𝑛 = 2 + 𝑛 2 3 7. 2 5 , 1 15 , −4 15 ,… 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 + ( ) + 0 + … + 30 −3 2 Find the sums of the following arithmetic series in summation notation. 22. 23. 24. 25. 26. 27. 28. How many terms of the arithmetic sequence -2, 3, 8,… must be added to get 1573? 29. How many terms of the arithmetic sequence 15, 12, 9,…must be added to get -39? 30. How many terms of the arithmetic sequence -1, 2, 5,… must be added to get 609? Answers 1. 21, 34, 47, 60, 73; Arithmetic; d = 13 3. 3, 6, 11, 20, 37; Not Arithmetic 6. 𝑎𝑛 = 2 3 𝑛− 2 3 ; 𝑎20 = 38 3 1 2 2. 4. , 1 3 , 1 4 , 1 5 1 3 𝑛+ 11 15 ; 𝑎20 =− 1 6 ; Not Arithmetic 5. an = 2n – 8 ; a20 = 32 an = 3n – 1; a20 = 59 7. 𝑎𝑛 =− , 89 15 8. an = 5n – 9 9. an = -3n + 103 10. an = -15n + 265 11. an = -7n + 4 12. an = -1.725n + 24.175 13. an = 2.5n + 3.5 14. S10 = 620 15. S50 = 4,600 16. S25 = 4,000 17. S88 = 3,106.4 18. S12 = 168 19. S8 = 660 20. S12 = 123 22. S50 = 1,275 23. S50 = 7,550 24. S426 = 125,031 25. S151 = 64,175 26. S = 355 27. S = 259 28. n = 26 29. n = 13 21. 𝑆23 = 621 2 30. n = 21