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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 127 · 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.Which term of the AP 4, 13, 22, 31, … is 130? (a) 17th (b) 15th (c) 16th (d) 14th
  2. 2.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 10 (b) 14 (c) 11 (d) 9
  3. 3.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 34 (b) 212 (c) 209 (d) 418
  4. 4.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 39 (c) 210 (d) 400
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 33 (d) 153
  6. 6.What is the 26th term of the AP 17, 24, 31, 38, …? (a) 175 (b) 182 (c) 192 (d) 199
  7. 7.Which term of the AP 17, 20, 23, 26, … is 53? (a) 13th (b) 15th (c) 14th (d) 12th
  8. 8.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 120 (c) 272 (d) 136
  9. 9.Which term of the AP 19, 22, 25, 28, … is 88? (a) 26th (b) 24th (c) 25th (d) 23rd
  10. 10.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 5112 (c) 2485 (d) 2557
  11. 11.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 20 (b) 12 (c) 14 (d) 13
  12. 12.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 130 (b) 120 (c) 21 (d) 240
  13. 13.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 156 (c) 72 (d) 78
  14. 14.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 4278 (c) 8742 (d) 4371
  15. 15.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 336 (b) 168 (c) 184 (d) 35
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 15 (d) 72
  17. 17.What is the 40th term of the AP 19, 22, 25, 28, …? (a) 117 (b) 139 (c) 136 (d) 120
  18. 18.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 68 (b) 456 (c) 840 (d) 420
  19. 19.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 18 (b) 16 (c) 14 (d) 15
  20. 20.Which term of the AP 1, 4, 7, 10, … is 43? (a) 14th (b) 17th (c) 16th (d) 15th
  21. 21.What is the 35th term of the AP 10, 16, 22, 28, …? (a) 220 (b) 204 (c) 214 (d) 210
  22. 22.What is the 10th term of the AP 4, 12, 20, 28, …? (a) 80 (b) 72 (c) 84 (d) 76
  23. 23.What is the 38th term of the AP 5, 13, 21, 29, …? (a) 309 (b) 296 (c) 304 (d) 301
  24. 24.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 22 (b) 23 (c) 20 (d) 21
  25. 25.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1770 (c) 1711 (d) 1771
  26. 26.Which term of the AP 4, 8, 12, 16, … is 44? (a) 10th (b) 13th (c) 12th (d) 11th
  27. 27.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 333 (b) 612 (c) 306 (d) 58
  28. 28.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 53 (b) 100 (c) 16 (d) 50
  29. 29.What is the 40th term of the AP 11, 20, 29, 38, …? (a) 351 (b) 371 (c) 360 (d) 362
  30. 30.What is the 11th term of the AP 9, 12, 15, 18, …? (a) 42 (b) 33 (c) 30 (d) 39
  31. 31.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 23 (b) 21 (c) 25 (d) 22
  32. 32.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 49 (b) 638 (c) 341 (d) 319
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 132 (d) 66
  34. 34.What is the 14th term of the AP 9, 16, 23, 30, …? (a) 91 (b) 98 (c) 107 (d) 100
  35. 35.What is the 35th term of the AP 7, 16, 25, 34, …? (a) 322 (b) 306 (c) 315 (d) 313
  36. 36.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 144 (b) 72 (c) 22 (d) 84
  37. 37.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 264 (b) 150 (c) 37 (d) 132
  38. 38.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 14 (b) 12 (c) 13 (d) 19
  39. 39.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 30 (b) 26 (c) 24 (d) 25
  40. 40.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 34 (b) 160 (c) 176 (d) 320

Answer key

  1. 15th
  2. 10
  3. 209
  4. 400
  5. 289
  6. 192
  7. 13th
  8. 136
  9. 24th
  10. 2556
  11. 13
  12. 120
  13. 78
  14. 4371
  15. 168
  16. 64
  17. 136
  18. 420
  19. 15
  20. 15th
  21. 214
  22. 76
  23. 301
  24. 21
  25. 1770
  26. 11th
  27. 306
  28. 50
  29. 362
  30. 39
  31. 22
  32. 319
  33. 121
  34. 100
  35. 313
  36. 72
  37. 132
  38. 13
  39. 25
  40. 160

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