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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 71 · 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 missing term in the AP 4, ?, 8, 10, 12? (a) 7 (b) 5 (c) 6 (d) 8
  2. 2.What is the 28th term of the AP 18, 26, 34, 42, …? (a) 224 (b) 216 (c) 234 (d) 242
  3. 3.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 43 (d) 484
  4. 4.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 297 (c) 594 (d) 302
  5. 5.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 130 (c) 240 (d) 21
  6. 6.What is the 40th term of the AP 1, 4, 7, 10, …? (a) 117 (b) 118 (c) 120 (d) 121
  7. 7.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 3422 (c) 1711 (d) 1653
  8. 8.Which term of the AP 6, 12, 18, 24, … is 78? (a) 14th (b) 15th (c) 13th (d) 12th
  9. 9.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 16 (b) 60 (c) 120 (d) 65
  10. 10.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 336 (c) 168 (d) 39
  11. 11.What is the 17th term of the AP 1, 10, 19, 28, …? (a) 154 (b) 145 (c) 144 (d) 153
  12. 12.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 2146 (c) 2145 (d) 4290
  13. 13.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 126 (b) 228 (c) 114 (d) 29
  14. 14.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 414 (b) 43 (c) 207 (d) 212
  15. 15.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 266 (b) 261 (c) 49 (d) 522
  16. 16.What is the 19th term of the AP 2, 5, 8, 11, …? (a) 59 (b) 54 (c) 56 (d) 57
  17. 17.What is the 12th term of the AP 9, 14, 19, 24, …? (a) 69 (b) 55 (c) 64 (d) 60
  18. 18.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4754 (c) 9506 (d) 4656
  19. 19.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 50 (c) 55 (d) 45
  20. 20.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 435 (c) 450 (d) 465
  21. 21.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1770 (c) 1771 (d) 1711
  22. 22.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4561 (c) 9120 (d) 4465
  23. 23.What is the 23rd term of the AP 13, 17, 21, 25, …? (a) 105 (b) 92 (c) 88 (d) 101
  24. 24.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 289 (d) 153
  25. 25.What is the 17th term of the AP 11, 17, 23, 29, …? (a) 96 (b) 107 (c) 102 (d) 113
  26. 26.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 26 (b) 30 (c) 27 (d) 25
  27. 27.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 180 (b) 34 (c) 162 (d) 324
  28. 28.What is the 18th term of the AP 15, 23, 31, 39, …? (a) 159 (b) 151 (c) 136 (d) 144
  29. 29.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 34 (b) 228 (c) 132 (d) 114
  30. 30.What is the 32nd term of the AP 19, 26, 33, 40, …? (a) 217 (b) 243 (c) 236 (d) 224
  31. 31.Which term of the AP 7, 12, 17, 22, … is 92? (a) 19th (b) 17th (c) 18th (d) 20th
  32. 32.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 562 (c) 561 (d) 528
  33. 33.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 9312 (c) 4656 (d) 4560
  34. 34.Which term of the AP 9, 12, 15, 18, … is 123? (a) 41st (b) 39th (c) 38th (d) 40th
  35. 35.What is the sum of all the whole numbers from 1 to 51? (a) 1326 (b) 1327 (c) 1275 (d) 2652
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  37. 37.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1596 (c) 3192 (d) 1568
  38. 38.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 9 (b) 7 (c) 8 (d) 10
  39. 39.What is the 14th term of the AP 20, 22, 24, 26, …? (a) 46 (b) 28 (c) 26 (d) 48
  40. 40.What is the 12th term of the AP 4, 8, 12, 16, …? (a) 52 (b) 44 (c) 48 (d) 49

Answer key

  1. 6
  2. 234
  3. 484
  4. 297
  5. 120
  6. 118
  7. 1711
  8. 13th
  9. 60
  10. 168
  11. 145
  12. 2145
  13. 114
  14. 207
  15. 261
  16. 56
  17. 64
  18. 4753
  19. 55
  20. 465
  21. 1770
  22. 4560
  23. 101
  24. 289
  25. 107
  26. 26
  27. 162
  28. 151
  29. 114
  30. 236
  31. 18th
  32. 561
  33. 4656
  34. 39th
  35. 1326
  36. 144
  37. 1596
  38. 8
  39. 46
  40. 48

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