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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 47 · 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 16, 25, 34, 43, … is 340? (a) 39th (b) 36th (c) 37th (d) 38th
  2. 2.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 1190 (c) 578 (d) 595
  3. 3.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 30 (b) 28 (c) 35 (d) 29
  4. 4.What is the 37th term of the AP 1, 10, 19, 28, …? (a) 334 (b) 333 (c) 324 (d) 325
  5. 5.What is the 40th term of the AP 16, 20, 24, 28, …? (a) 160 (b) 172 (c) 156 (d) 176
  6. 6.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 264 (c) 133 (d) 132
  7. 7.What is the 15th term of the AP 17, 23, 29, 35, …? (a) 84 (b) 107 (c) 90 (d) 101
  8. 8.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 35 (b) 43 (c) 36 (d) 34
  9. 9.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 700 (b) 62 (c) 380 (d) 350
  10. 10.Which term of the AP 17, 20, 23, 26, … is 131? (a) 40th (b) 41st (c) 39th (d) 38th
  11. 11.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 406 (d) 784
  12. 12.What is the 32nd term of the AP 12, 20, 28, 36, …? (a) 260 (b) 248 (c) 268 (d) 256
  13. 13.What is the 39th term of the AP 7, 15, 23, 31, …? (a) 311 (b) 312 (c) 319 (d) 304
  14. 14.What is the 17th term of the AP 15, 17, 19, 21, …? (a) 32 (b) 47 (c) 34 (d) 49
  15. 15.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2415 (c) 2485 (d) 4970
  16. 16.What is the 14th term of the AP 19, 27, 35, 43, …? (a) 112 (b) 123 (c) 131 (d) 104
  17. 17.What is the 37th term of the AP 4, 10, 16, 22, …? (a) 222 (b) 216 (c) 226 (d) 220
  18. 18.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  19. 19.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 4 (c) 5 (d) 3
  20. 20.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3362 (c) 3403 (d) 3321
  21. 21.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 240 (b) 264 (c) 480 (d) 51
  22. 22.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 625 (d) 49
  23. 23.What is the 16th term of the AP 2, 6, 10, 14, …? (a) 62 (b) 60 (c) 64 (d) 66
  24. 24.What is the sum of all the whole numbers from 1 to 39? (a) 1560 (b) 780 (c) 781 (d) 741
  25. 25.What is the 24th term of the AP 5, 7, 9, 11, …? (a) 48 (b) 46 (c) 51 (d) 53
  26. 26.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 676 (d) 51
  27. 27.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 372 (b) 53 (c) 744 (d) 396
  28. 28.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 436 (d) 406
  29. 29.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 27 (b) 192 (c) 204 (d) 384
  30. 30.Which term of the AP 5, 8, 11, 14, … is 53? (a) 19th (b) 16th (c) 18th (d) 17th
  31. 31.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  32. 32.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 324 (c) 612 (d) 42
  33. 33.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 4372 (c) 4278 (d) 8742
  34. 34.Which term of the AP 14, 18, 22, 26, … is 74? (a) 17th (b) 18th (c) 16th (d) 15th
  35. 35.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 21 (b) 15 (c) 14 (d) 16
  36. 36.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 638 (b) 319 (c) 54 (d) 324
  37. 37.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 297 (b) 54 (c) 540 (d) 270
  38. 38.What is the 18th term of the AP 10, 14, 18, 22, …? (a) 82 (b) 78 (c) 68 (d) 72
  39. 39.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 9 (b) 11 (c) 8 (d) 7
  40. 40.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 456 (b) 240 (c) 228 (d) 30

Answer key

  1. 37th
  2. 595
  3. 29
  4. 325
  5. 172
  6. 132
  7. 101
  8. 35
  9. 350
  10. 39th
  11. 784
  12. 260
  13. 311
  14. 47
  15. 2485
  16. 123
  17. 220
  18. 196
  19. 4
  20. 3403
  21. 240
  22. 625
  23. 62
  24. 780
  25. 51
  26. 676
  27. 372
  28. 435
  29. 192
  30. 17th
  31. 529
  32. 306
  33. 4371
  34. 16th
  35. 15
  36. 319
  37. 270
  38. 78
  39. 8
  40. 228

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