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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 366 · 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 all the whole numbers from 1 to 10? (a) 110 (b) 55 (c) 45 (d) 50
  2. 2.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 480 (b) 70 (c) 888 (d) 444
  3. 3.Which term of the AP 2, 5, 8, 11, … is 80? (a) 26th (b) 28th (c) 29th (d) 27th
  4. 4.What is the 38th term of the AP 11, 20, 29, 38, …? (a) 342 (b) 333 (c) 344 (d) 353
  5. 5.What is the 16th term of the AP 13, 21, 29, 37, …? (a) 128 (b) 141 (c) 120 (d) 133
  6. 6.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 108 (b) 216 (c) 16 (d) 109
  7. 7.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 36 (b) 28 (c) 27 (d) 26
  8. 8.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 20 (b) 19 (c) 26 (d) 18
  9. 9.What is the 25th term of the AP 9, 13, 17, 21, …? (a) 109 (b) 100 (c) 96 (d) 105
  10. 10.Which term of the AP 14, 23, 32, 41, … is 212? (a) 24th (b) 25th (c) 23rd (d) 22nd
  11. 11.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 9 (b) 8 (c) 10 (d) 7
  12. 12.What is the 11th term of the AP 6, 12, 18, 24, …? (a) 72 (b) 66 (c) 67 (d) 60
  13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 378 (d) 729
  14. 14.What is the 14th term of the AP 8, 14, 20, 26, …? (a) 86 (b) 78 (c) 84 (d) 92
  15. 15.What is the 10th term of the AP 2, 9, 16, 23, …? (a) 65 (b) 72 (c) 63 (d) 70
  16. 16.Which term of the AP 14, 21, 28, 35, … is 210? (a) 29th (b) 28th (c) 31st (d) 30th
  17. 17.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 231 (c) 462 (d) 41
  18. 18.Which term of the AP 6, 14, 22, 30, … is 110? (a) 16th (b) 14th (c) 15th (d) 13th
  19. 19.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 168 (b) 180 (c) 336 (d) 25
  20. 20.Which term of the AP 1, 7, 13, 19, … is 61? (a) 13th (b) 10th (c) 12th (d) 11th
  21. 21.What is the 34th term of the AP 14, 16, 18, 20, …? (a) 68 (b) 66 (c) 80 (d) 82
  22. 22.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1152 (c) 1128 (d) 1176
  23. 23.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 300 (b) 324 (c) 47 (d) 600
  24. 24.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 32 (b) 31 (c) 33 (d) 38
  25. 25.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 266 (b) 133 (c) 34 (d) 138
  26. 26.What is the 37th term of the AP 12, 14, 16, 18, …? (a) 74 (b) 84 (c) 86 (d) 72
  27. 27.Which term of the AP 13, 18, 23, 28, … is 48? (a) 7th (b) 8th (c) 9th (d) 10th
  28. 28.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 47 (d) 600
  29. 29.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 90 (b) 46 (c) 9 (d) 45
  30. 30.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4418 (c) 8930 (d) 4371
  31. 31.What is the 35th term of the AP 1, 3, 5, 7, …? (a) 69 (b) 68 (c) 70 (d) 71
  32. 32.What is the 34th term of the AP 6, 15, 24, 33, …? (a) 303 (b) 306 (c) 312 (d) 297
  33. 33.What is the 18th term of the AP 1, 8, 15, 22, …? (a) 126 (b) 120 (c) 119 (d) 127
  34. 34.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 270 (b) 288 (c) 39 (d) 540
  35. 35.What is the 40th term of the AP 8, 10, 12, 14, …? (a) 78 (b) 86 (c) 88 (d) 80
  36. 36.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 25 (b) 18 (c) 17 (d) 16
  37. 37.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  38. 38.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 17 (d) 45
  39. 39.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4371 (c) 4278 (d) 4372
  40. 40.What is the 40th term of the AP 20, 26, 32, 38, …? (a) 234 (b) 260 (c) 240 (d) 254

Answer key

  1. 55
  2. 444
  3. 27th
  4. 344
  5. 133
  6. 108
  7. 27
  8. 19
  9. 105
  10. 23rd
  11. 8
  12. 66
  13. 729
  14. 86
  15. 65
  16. 29th
  17. 441
  18. 14th
  19. 168
  20. 11th
  21. 80
  22. 1176
  23. 300
  24. 32
  25. 133
  26. 84
  27. 8th
  28. 576
  29. 45
  30. 4465
  31. 69
  32. 303
  33. 120
  34. 270
  35. 86
  36. 17
  37. 196
  38. 81
  39. 4371
  40. 254

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