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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 638 · 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 8, ?, 20, 26, 32? (a) 15 (b) 13 (c) 20 (d) 14
  2. 2.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 2775 (c) 2851 (d) 5700
  3. 3.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 11 (b) 17 (c) 12 (d) 13
  4. 4.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 130 (b) 65 (c) 25 (d) 80
  5. 5.Which term of the AP 12, 18, 24, 30, … is 210? (a) 36th (b) 35th (c) 33rd (d) 34th
  6. 6.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 49 (b) 648 (c) 348 (d) 324
  7. 7.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 348 (b) 372 (c) 696 (d) 51
  8. 8.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 33 (b) 168 (c) 304 (d) 152
  9. 9.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1711 (c) 1770 (d) 3540
  10. 10.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 1560 (c) 781 (d) 741
  11. 11.What is the 30th term of the AP 9, 18, 27, 36, …? (a) 279 (b) 261 (c) 270 (d) 271
  12. 12.What is the 32nd term of the AP 17, 21, 25, 29, …? (a) 145 (b) 141 (c) 128 (d) 124
  13. 13.What is the 18th term of the AP 6, 9, 12, 15, …? (a) 60 (b) 54 (c) 57 (d) 51
  14. 14.What is the 23rd term of the AP 19, 27, 35, 43, …? (a) 203 (b) 184 (c) 176 (d) 195
  15. 15.What is the 21st term of the AP 15, 24, 33, 42, …? (a) 195 (b) 204 (c) 180 (d) 189
  16. 16.What is the 38th term of the AP 17, 22, 27, 32, …? (a) 185 (b) 202 (c) 190 (d) 207
  17. 17.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 702 (d) 351
  18. 18.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 8 (c) 9 (d) 10
  19. 19.What is the 15th term of the AP 20, 22, 24, 26, …? (a) 30 (b) 48 (c) 28 (d) 50
  20. 20.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 90 (b) 81 (c) 21 (d) 162
  21. 21.Which term of the AP 15, 21, 27, 33, … is 165? (a) 28th (b) 26th (c) 27th (d) 25th
  22. 22.Which term of the AP 12, 15, 18, 21, … is 66? (a) 19th (b) 20th (c) 18th (d) 22nd
  23. 23.What is the sum of the first 10 terms of the AP 10, 15, 20, …? (a) 55 (b) 350 (c) 325 (d) 650
  24. 24.What is the 26th term of the AP 4, 11, 18, 25, …? (a) 186 (b) 182 (c) 175 (d) 179
  25. 25.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2485 (c) 2556 (d) 2557
  26. 26.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 39 (d) 420
  27. 27.What is the missing term in the AP 15, 24, 33, ?, 51? (a) 42 (b) 41 (c) 51 (d) 43
  28. 28.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 270 (b) 18 (c) 140 (d) 135
  29. 29.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 2862 (c) 1378 (d) 1431
  30. 30.Which term of the AP 14, 18, 22, 26, … is 54? (a) 12th (b) 10th (c) 13th (d) 11th
  31. 31.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 126 (b) 228 (c) 29 (d) 114
  32. 32.What is the 22nd term of the AP 16, 19, 22, 25, …? (a) 66 (b) 79 (c) 63 (d) 82
  33. 33.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 24 (b) 26 (c) 32 (d) 25
  34. 34.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1800 (c) 1830 (d) 1770
  35. 35.What is the 22nd term of the AP 20, 27, 34, 41, …? (a) 174 (b) 147 (c) 167 (d) 154
  36. 36.What is the 23rd term of the AP 10, 16, 22, 28, …? (a) 148 (b) 142 (c) 138 (d) 132
  37. 37.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 841 (d) 870
  38. 38.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 22 (b) 72 (c) 144 (d) 84
  39. 39.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 272 (c) 136 (d) 128
  40. 40.What is the 26th term of the AP 12, 18, 24, 30, …? (a) 150 (b) 162 (c) 156 (d) 168

Answer key

  1. 14
  2. 2850
  3. 12
  4. 65
  5. 34th
  6. 324
  7. 348
  8. 152
  9. 1770
  10. 780
  11. 270
  12. 141
  13. 57
  14. 195
  15. 195
  16. 202
  17. 351
  18. 8
  19. 48
  20. 81
  21. 26th
  22. 19th
  23. 325
  24. 179
  25. 2556
  26. 400
  27. 42
  28. 135
  29. 1431
  30. 11th
  31. 114
  32. 79
  33. 25
  34. 1830
  35. 167
  36. 142
  37. 841
  38. 72
  39. 136
  40. 162

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