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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 79 · 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 12 terms of the AP 8, 9, 10, …? (a) 324 (b) 168 (c) 162 (d) 19
  2. 2.What is the 12th term of the AP 3, 12, 21, 30, …? (a) 99 (b) 111 (c) 108 (d) 102
  3. 3.What is the 39th term of the AP 20, 25, 30, 35, …? (a) 190 (b) 195 (c) 210 (d) 215
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 72 (d) 36
  5. 5.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 24 (b) 23 (c) 22 (d) 26
  6. 6.Which term of the AP 2, 5, 8, 11, … is 38? (a) 15th (b) 12th (c) 13th (d) 14th
  7. 7.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 57 (b) 704 (c) 352 (d) 357
  8. 8.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 4692 (c) 2278 (d) 2346
  9. 9.What is the 28th term of the AP 17, 25, 33, 41, …? (a) 216 (b) 224 (c) 233 (d) 241
  10. 10.What is the 32nd term of the AP 15, 19, 23, 27, …? (a) 128 (b) 143 (c) 139 (d) 124
  11. 11.Which term of the AP 3, 7, 11, 15, … is 115? (a) 31st (b) 29th (c) 30th (d) 28th
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 13 (d) 56
  13. 13.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 2416 (c) 2415 (d) 4830
  14. 14.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 19 (b) 20 (c) 24 (d) 21
  15. 15.What is the 24th term of the AP 5, 8, 11, 14, …? (a) 77 (b) 72 (c) 69 (d) 74
  16. 16.What is the 11th term of the AP 6, 9, 12, 15, …? (a) 30 (b) 36 (c) 33 (d) 39
  17. 17.What is the 39th term of the AP 14, 18, 22, 26, …? (a) 156 (b) 166 (c) 152 (d) 170
  18. 18.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  19. 19.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 31 (c) 133 (d) 147
  20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 462 (d) 41
  21. 21.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 9 (b) 7 (c) 12 (d) 8
  22. 22.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 110 (c) 95 (d) 190
  23. 23.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 143 (b) 286 (c) 18 (d) 144
  24. 24.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 5 (b) 4 (c) 2 (d) 3
  25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  26. 26.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 438 (b) 468 (c) 876 (d) 64
  27. 27.What is the 37th term of the AP 8, 14, 20, 26, …? (a) 216 (b) 224 (c) 222 (d) 230
  28. 28.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1596 (c) 1568 (d) 3192
  29. 29.Which term of the AP 10, 15, 20, 25, … is 200? (a) 41st (b) 40th (c) 38th (d) 39th
  30. 30.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 144 (b) 258 (c) 129 (d) 34
  31. 31.What is the 37th term of the AP 20, 28, 36, 44, …? (a) 296 (b) 316 (c) 288 (d) 308
  32. 32.Which term of the AP 6, 8, 10, 12, … is 52? (a) 25th (b) 26th (c) 24th (d) 23rd
  33. 33.What is the 13th term of the AP 16, 23, 30, 37, …? (a) 100 (b) 107 (c) 84 (d) 91
  34. 34.What is the 37th term of the AP 1, 4, 7, 10, …? (a) 112 (b) 111 (c) 109 (d) 108
  35. 35.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 44 (c) 184 (d) 208
  36. 36.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 12 (b) 19 (c) 14 (d) 13
  37. 37.What is the 36th term of the AP 18, 24, 30, 36, …? (a) 210 (b) 216 (c) 234 (d) 228
  38. 38.What is the 11th term of the AP 9, 11, 13, 15, …? (a) 20 (b) 22 (c) 31 (d) 29
  39. 39.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
  40. 40.What is the 13th term of the AP 6, 14, 22, 30, …? (a) 104 (b) 96 (c) 102 (d) 110

Answer key

  1. 162
  2. 102
  3. 210
  4. 64
  5. 23
  6. 13th
  7. 352
  8. 2346
  9. 233
  10. 139
  11. 29th
  12. 49
  13. 2415
  14. 20
  15. 74
  16. 36
  17. 166
  18. 400
  19. 133
  20. 441
  21. 8
  22. 95
  23. 143
  24. 3
  25. 729
  26. 438
  27. 224
  28. 1596
  29. 39th
  30. 129
  31. 308
  32. 24th
  33. 100
  34. 109
  35. 184
  36. 13
  37. 228
  38. 29
  39. 196
  40. 102

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