University:
Carleton College
Course:
MATH 111 | Introduction to Calculus
Academic year:

2024
Views:

462

Pages:

4
Author:

StellarSymphony

11.1 – 11.3 Quiz Review Pre-Calculus Name________________ Find the first five terms of the sequence. 1. 𝑎𝑛 = 3𝑛(𝑛 + 5) 2. 𝑎𝑛 = 3𝑎𝑛−1 +6 , 𝑎1 3 = −8 3. 𝑎𝑛 = −5𝑎𝑛−1 , 𝑎1 = 3 Find the sum of the sequence. 5 7 4. ∑ 2𝑘 5. ∑(3𝑘 2 − 6𝑘) 2 𝑘=0 𝑘=2 4 6. ∑ (𝑘 ) 2 𝑘=1 Write the sum using sigma notation. Hint: are any of these arithmetic or geometric?? 7. 5 5 5 + 1+2 + 1+3 + 1+1 5 ⋯ + 1 + 16 8. 6 + 13 + 20 + 27 + ⋯ + 97 9. 3 − 9 + 27 − 81 + 243 − 729 Determine whether the sequence is arithmetic or geometric, then find the nth term of the sequence. 1 1 10. 10, 8, 6, 4, 2…. 11. 5, 1, 0.2, 0.04, … 12. 4 , 2 , 1, 2, 4, … 1 13. 1, − 2 , 1 , 4 1 −8,… 14. 3.7, 4.3, 4.9, 5.5, 6.1,…. 15. -6, -2, 2, … Find the indicated term of the arithmetic sequence. 16. Find 𝑎27 if 𝑎10 = 115 and 𝑎5 = 190 17. Find 𝑎43 if 𝑎3 = 13 and 𝑎10 = 41 Write a rule for the nth term of the arithmetic sequence. 18. 𝑎6 = 85, 𝑎3 = 94 19. 𝑎4 = 112, 𝑎21 = 61 20. Which term of the arithmetic sequence -1, 4, 9, … is 374? 21. Which term of the arithmetic sequence -0.3, 1.8, 3.9, … is 1186.2? Find the indicated term of the geometric sequence. 22. Find 𝑎12 if 𝑎6 = 3 and 𝑟 = 2 23. Find 𝑎2 if 𝑎4 = 500 and 𝑟 = 5 Write a rule for the nth term of the geometric sequence. 24. 𝑎3 = 12, 𝑎1 = 3 25. 𝑎8 = −8748, 𝑎1 = 4 Find the partial sum 𝑺𝒏 of the arithmetic sequence with the given conditions. 26. a1 = 4, d = -3, n = 15 Find the sum of the arithmetic series. 28. -6 – 2 + 2 + …+222 1 27. a1 = 12, d = 3, n = 13 150 29. ∑(11 + 2𝑘) 𝑘=1 300 30. ∑(7𝑘 − 3) 31. 16 + 10 + 4 +⋯+(-50) 𝑘=1 32. The first term of an arithmetic sequence is -1 and the third term is 9. How many terms of this sequence must be added to get 132? 33. The first term of an arithmetic sequence is 7 and the fourth term is 28. How many terms of this sequence must be added to get 735? Find the sum of the geometric series. 20 3 2 35. 12 + 6 + 3 + + 34. 5 + 10 + 20 + … + 10,240 3 ⋯ + 256 36. ∑(3 ∙ 2𝑛−1 ) 𝑘=1 Find the sum of the infinite geometric series. 1 1 1 37. − 8 − 12 − 18 + ⋯ 38. 4 4 +9 15 20 + 27 + 100 + 81 ⋯ Express the decimal as a fraction. YOU MUST SHOW WORK!!!!!!!!!!!!!!!!!!!! ̅̅̅̅̅ 39. 0. 625 ̅̅̅̅̅ 40. 0.2777 Answers 1. 18, 42, 72, 108, 150 2. -8, -6, -4, -2, 0 16 5. 75 6. 5 7. ∑ ( 𝑘=1 5 ) 1+𝑘 1 𝑛−1 3. 3, -15, 75, -375, 1875 4. 278 14 8. 6 ∑(7𝑘 − 1) 𝑘=1 1 9. ∑(−1)𝑘−1 (3𝑘 ) 𝑘=1 1 𝑛−1 2 10. 𝑎𝑛 = −2𝑛 + 12 11. 𝑎𝑛 = 5 (5) 12. 𝑎𝑛 = 4 (2)𝑛−1 13. 𝑎𝑛 = 1 (− ) 14. 𝑎𝑛 = 0.6𝑛 + 3.1 15. 𝑎𝑛 = 4𝑛 − 10 16. 𝑎27 = −140 17. 𝑎43 = 173 18. 𝑎𝑛 = −3𝑛 + 103 19. 𝑎𝑛 = −3𝑛 + 124 20. n = 76 21. n = 566 22. 𝑎12 = 192 23. 𝑎2 = 20 24. 𝑎𝑛 = 3(2)𝑛−1 and 𝑎𝑛 = 3(−2)𝑛−1 25. 𝑎𝑛 = 4(−3)𝑛−1 26. 𝑆15 = −255 27. 𝑆13 = 182 28. 𝑆58 = 6264 29. 𝑆150 = 24,300 30. 𝑆300 = 315,150 31. 𝑆12 = −204 32. n = 8 33. n = 14 34. 𝑆12 = 20,475 35. 𝑆11 = 38. Sum DNE 39. 3 37. 𝑆 = − 8 625 999 6141 256 36. 𝑆20 = 3,145,725 40. 5 18