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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 786 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 121 (d) 120
  2. 2.What is the 16th term of the AP 10, 16, 22, 28, …? (a) 96 (b) 106 (c) 100 (d) 90
  3. 3.What is the 15th term of the AP 6, 8, 10, 12, …? (a) 36 (b) 28 (c) 34 (d) 30
  4. 4.What is the 30th term of the AP 6, 14, 22, 30, …? (a) 240 (b) 238 (c) 246 (d) 232
  5. 5.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 140 (b) 70 (c) 71 (d) 13
  6. 6.What is the 17th term of the AP 13, 15, 17, 19, …? (a) 34 (b) 45 (c) 32 (d) 47
  7. 7.What is the 31st term of the AP 1, 10, 19, 28, …? (a) 280 (b) 270 (c) 271 (d) 279
  8. 8.What is the 31st term of the AP 15, 22, 29, 36, …? (a) 217 (b) 225 (c) 210 (d) 232
  9. 9.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2556 (c) 5112 (d) 2485
  10. 10.Which term of the AP 10, 12, 14, 16, … is 50? (a) 20th (b) 25th (c) 21st (d) 22nd
  11. 11.What is the 40th term of the AP 5, 7, 9, 11, …? (a) 80 (b) 78 (c) 83 (d) 85
  12. 12.What is the 36th term of the AP 4, 13, 22, 31, …? (a) 319 (b) 324 (c) 315 (d) 328
  13. 13.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 1560 (c) 741 (d) 780
  14. 14.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 55 (c) 10 (d) 110
  15. 15.Which term of the AP 7, 15, 23, 31, … is 111? (a) 13th (b) 16th (c) 15th (d) 14th
  16. 16.What is the 23rd term of the AP 18, 22, 26, 30, …? (a) 110 (b) 106 (c) 92 (d) 88
  17. 17.Which term of the AP 16, 18, 20, 22, … is 40? (a) 14th (b) 13th (c) 20th (d) 12th
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
  19. 19.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 8010 (c) 4005 (d) 4006
  20. 20.What is the 11th term of the AP 7, 13, 19, 25, …? (a) 66 (b) 73 (c) 67 (d) 60
  21. 21.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 132 (c) 121 (d) 21
  22. 22.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 820 (c) 800 (d) 1640
  23. 23.What is the missing term in the AP 18, 23, ?, 33, 38? (a) 28 (b) 27 (c) 29 (d) 33
  24. 24.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 11 (b) 12 (c) 9 (d) 10
  25. 25.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 230 (c) 210 (d) 39
  26. 26.Which term of the AP 1, 4, 7, 10, … is 28? (a) 12th (b) 9th (c) 10th (d) 11th
  27. 27.What is the 37th term of the AP 16, 19, 22, 25, …? (a) 111 (b) 124 (c) 127 (d) 108
  28. 28.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 66 (c) 132 (d) 55
  29. 29.What is the 19th term of the AP 9, 13, 17, 21, …? (a) 81 (b) 72 (c) 76 (d) 85
  30. 30.Which term of the AP 4, 7, 10, 13, … is 118? (a) 38th (b) 40th (c) 41st (d) 39th
  31. 31.What is the 16th term of the AP 10, 13, 16, 19, …? (a) 58 (b) 45 (c) 48 (d) 55
  32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 78 (d) 23
  33. 33.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1770 (c) 3660 (d) 1830
  34. 34.What is the 11th term of the AP 15, 23, 31, 39, …? (a) 88 (b) 80 (c) 95 (d) 103
  35. 35.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 870 (d) 57
  36. 36.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 36 (b) 296 (c) 168 (d) 148
  37. 37.What is the 24th term of the AP 1, 8, 15, 22, …? (a) 162 (b) 169 (c) 168 (d) 161
  38. 38.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 28 (b) 23 (c) 24 (d) 25
  39. 39.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 18 (b) 17 (c) 16 (d) 21
  40. 40.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 59 (d) 900

Answer key

  1. 120
  2. 100
  3. 34
  4. 238
  5. 70
  6. 45
  7. 271
  8. 225
  9. 2556
  10. 21st
  11. 83
  12. 319
  13. 780
  14. 55
  15. 14th
  16. 106
  17. 13th
  18. 81
  19. 4005
  20. 67
  21. 121
  22. 820
  23. 28
  24. 10
  25. 210
  26. 10th
  27. 124
  28. 66
  29. 81
  30. 39th
  31. 55
  32. 144
  33. 1830
  34. 95
  35. 841
  36. 148
  37. 162
  38. 24
  39. 17
  40. 900

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