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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 137 · 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 the first 7 terms of the AP 2, 3, 4, …? (a) 8 (b) 35 (c) 70 (d) 36
  2. 2.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 15 (c) 63 (d) 70
  3. 3.Which term of the AP 9, 12, 15, 18, … is 111? (a) 34th (b) 36th (c) 37th (d) 35th
  4. 4.What is the 29th term of the AP 20, 27, 34, 41, …? (a) 216 (b) 196 (c) 223 (d) 203
  5. 5.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 756 (c) 351 (d) 379
  6. 6.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 15 (b) 14 (c) 16 (d) 17
  7. 7.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 24 (b) 17 (c) 16 (d) 18
  8. 8.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 24 (b) 23 (c) 22 (d) 21
  9. 9.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 21 (b) 65 (c) 130 (d) 75
  10. 10.Which term of the AP 8, 17, 26, 35, … is 215? (a) 25th (b) 24th (c) 23rd (d) 26th
  11. 11.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 50 (c) 13 (d) 45
  12. 12.Which term of the AP 11, 17, 23, 29, … is 113? (a) 20th (b) 17th (c) 18th (d) 19th
  13. 13.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 17 (b) 12 (c) 11 (d) 13
  14. 14.What is the 19th term of the AP 3, 8, 13, 18, …? (a) 93 (b) 98 (c) 90 (d) 95
  15. 15.What is the 24th term of the AP 3, 10, 17, 24, …? (a) 161 (b) 168 (c) 164 (d) 171
  16. 16.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 703 (c) 722 (d) 1482
  17. 17.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 11 (c) 45 (d) 46
  18. 18.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 24 (b) 25 (c) 29 (d) 26
  19. 19.Which term of the AP 14, 16, 18, 20, … is 72? (a) 31st (b) 30th (c) 36th (d) 29th
  20. 20.What is the 12th term of the AP 4, 11, 18, 25, …? (a) 84 (b) 81 (c) 77 (d) 88
  21. 21.What is the 26th term of the AP 4, 12, 20, 28, …? (a) 204 (b) 200 (c) 212 (d) 208
  22. 22.Which term of the AP 1, 7, 13, 19, … is 49? (a) 11th (b) 10th (c) 8th (d) 9th
  23. 23.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 20 (b) 29 (c) 21 (d) 22
  24. 24.What is the 23rd term of the AP 17, 24, 31, 38, …? (a) 178 (b) 154 (c) 161 (d) 171
  25. 25.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 396 (b) 209 (c) 198 (d) 28
  26. 26.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 120 (b) 216 (c) 108 (d) 24
  27. 27.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 18 (c) 60 (d) 120
  28. 28.What is the 33rd term of the AP 18, 24, 30, 36, …? (a) 192 (b) 198 (c) 216 (d) 210
  29. 29.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 53 (b) 372 (c) 396 (d) 744
  30. 30.What is the 27th term of the AP 9, 14, 19, 24, …? (a) 144 (b) 135 (c) 139 (d) 130
  31. 31.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 54 (b) 30 (c) 7 (d) 27
  32. 32.Which term of the AP 17, 25, 33, 41, … is 305? (a) 39th (b) 36th (c) 38th (d) 37th
  33. 33.What is the 20th term of the AP 12, 17, 22, 27, …? (a) 95 (b) 112 (c) 100 (d) 107
  34. 34.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 324 (b) 180 (c) 162 (d) 34
  35. 35.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 37 (b) 38 (c) 39 (d) 44
  36. 36.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 270 (b) 243 (c) 486 (d) 51
  37. 37.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 45 (b) 42 (c) 46 (d) 49
  38. 38.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 68 (b) 456 (c) 840 (d) 420
  39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
  40. 40.What is the 18th term of the AP 5, 14, 23, 32, …? (a) 162 (b) 167 (c) 158 (d) 153

Answer key

  1. 35
  2. 63
  3. 35th
  4. 216
  5. 378
  6. 15
  7. 17
  8. 22
  9. 65
  10. 24th
  11. 45
  12. 18th
  13. 12
  14. 93
  15. 164
  16. 741
  17. 45
  18. 25
  19. 30th
  20. 81
  21. 204
  22. 9th
  23. 21
  24. 171
  25. 198
  26. 108
  27. 60
  28. 210
  29. 372
  30. 139
  31. 27
  32. 37th
  33. 107
  34. 162
  35. 38
  36. 243
  37. 46
  38. 420
  39. 484
  40. 158

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