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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 2 · 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 62? (a) 1953 (b) 3906 (c) 1922 (d) 1891
  2. 2.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 522 (b) 266 (c) 49 (d) 261
  3. 3.What is the 31st term of the AP 2, 5, 8, 11, …? (a) 92 (b) 93 (c) 95 (d) 90
  4. 4.What is the 32nd term of the AP 6, 8, 10, 12, …? (a) 70 (b) 64 (c) 62 (d) 68
  5. 5.Which term of the AP 13, 22, 31, 40, … is 328? (a) 37th (b) 38th (c) 36th (d) 35th
  6. 6.What is the 26th term of the AP 11, 19, 27, 35, …? (a) 211 (b) 200 (c) 208 (d) 219
  7. 7.Which term of the AP 9, 18, 27, 36, … is 162? (a) 17th (b) 19th (c) 20th (d) 18th
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 702 (d) 351
  9. 9.Which term of the AP 7, 16, 25, 34, … is 313? (a) 37th (b) 34th (c) 35th (d) 36th
  10. 10.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 43 (d) 253
  11. 11.What is the missing term in the AP 20, 23, 26, ?, 32? (a) 28 (b) 30 (c) 29 (d) 32
  12. 12.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 117 (b) 234 (c) 132 (d) 32
  13. 13.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 62 (b) 380 (c) 700 (d) 350
  14. 14.What is the 21st term of the AP 1, 9, 17, 25, …? (a) 160 (b) 169 (c) 161 (d) 168
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 39 (d) 210
  16. 16.What is the 14th term of the AP 20, 22, 24, 26, …? (a) 48 (b) 28 (c) 46 (d) 26
  17. 17.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 21 (b) 22 (c) 20 (d) 23
  18. 18.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 350 (c) 175 (d) 31
  19. 19.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 230 (b) 215 (c) 35 (d) 430
  20. 20.Which term of the AP 7, 16, 25, 34, … is 322? (a) 37th (b) 35th (c) 36th (d) 38th
  21. 21.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 800 (c) 820 (d) 1640
  22. 22.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 253 (c) 231 (d) 506
  23. 23.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 9 (b) 7 (c) 8 (d) 10
  24. 24.What is the 31st term of the AP 5, 7, 9, 11, …? (a) 67 (b) 62 (c) 60 (d) 65
  25. 25.What is the 10th term of the AP 1, 5, 9, 13, …? (a) 36 (b) 40 (c) 41 (d) 37
  26. 26.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 36 (b) 147 (c) 294 (d) 152
  27. 27.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 29 (b) 160 (c) 296 (d) 148
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  29. 29.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 10 (b) 9 (c) 11 (d) 14
  30. 30.Which term of the AP 5, 10, 15, 20, … is 115? (a) 24th (b) 22nd (c) 25th (d) 23rd
  31. 31.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 13 (b) 12 (c) 14 (d) 18
  32. 32.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 17 (b) 19 (c) 22 (d) 18
  33. 33.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 10 (b) 12 (c) 9 (d) 8
  34. 34.What is the missing term in the AP 11, 20, ?, 38, 47? (a) 38 (b) 29 (c) 30 (d) 28
  35. 35.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4754 (c) 4656 (d) 9506
  36. 36.Which term of the AP 8, 14, 20, 26, … is 242? (a) 39th (b) 40th (c) 41st (d) 42nd
  37. 37.What is the 20th term of the AP 5, 10, 15, 20, …? (a) 105 (b) 100 (c) 101 (d) 95
  38. 38.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 29 (c) 216 (d) 228
  39. 39.What is the 30th term of the AP 14, 18, 22, 26, …? (a) 130 (b) 116 (c) 120 (d) 134
  40. 40.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 105 (b) 210 (c) 114 (d) 25

Answer key

  1. 1953
  2. 261
  3. 92
  4. 68
  5. 36th
  6. 211
  7. 18th
  8. 676
  9. 35th
  10. 484
  11. 29
  12. 117
  13. 350
  14. 161
  15. 400
  16. 46
  17. 21
  18. 175
  19. 215
  20. 36th
  21. 820
  22. 253
  23. 8
  24. 65
  25. 37
  26. 147
  27. 148
  28. 841
  29. 10
  30. 23rd
  31. 13
  32. 18
  33. 9
  34. 29
  35. 4753
  36. 40th
  37. 100
  38. 216
  39. 130
  40. 105

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