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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 273 · 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 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  2. 2.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 24 (b) 23 (c) 25 (d) 29
  3. 3.What is the missing term in the AP 12, 21, ?, 39, 48? (a) 31 (b) 39 (c) 30 (d) 29
  4. 4.What is the 16th term of the AP 20, 28, 36, 44, …? (a) 128 (b) 120 (c) 148 (d) 140
  5. 5.What is the 32nd term of the AP 14, 17, 20, 23, …? (a) 110 (b) 107 (c) 96 (d) 93
  6. 6.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 374 (b) 64 (c) 407 (d) 748
  7. 7.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 14 (b) 22 (c) 13 (d) 12
  8. 8.What is the 36th term of the AP 8, 10, 12, 14, …? (a) 70 (b) 72 (c) 80 (d) 78
  9. 9.Which term of the AP 12, 18, 24, 30, … is 120? (a) 20th (b) 19th (c) 21st (d) 18th
  10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
  11. 11.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 25 (b) 115 (c) 112 (d) 224
  12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 9 (d) 25
  13. 13.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 9312 (c) 4656 (d) 4608
  14. 14.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 300 (d) 650
  15. 15.Which term of the AP 4, 10, 16, 22, … is 160? (a) 28th (b) 27th (c) 29th (d) 26th
  16. 16.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 4095 (c) 4005 (d) 8190
  17. 17.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 1152 (c) 2352 (d) 1128
  18. 18.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 25 (b) 26 (c) 24 (d) 23
  19. 19.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 216 (b) 44 (c) 221 (d) 432
  20. 20.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 28 (b) 27 (c) 36 (d) 26
  21. 21.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 34 (b) 43 (c) 35 (d) 36
  22. 22.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 24 (b) 23 (c) 22 (d) 26
  23. 23.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 496 (d) 1056
  24. 24.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 100 (b) 110 (c) 200 (d) 19
  25. 25.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 25 (c) 9 (d) 50
  26. 26.What is the 20th term of the AP 14, 18, 22, 26, …? (a) 94 (b) 80 (c) 90 (d) 76
  27. 27.What is the 27th term of the AP 2, 5, 8, 11, …? (a) 81 (b) 83 (c) 78 (d) 80
  28. 28.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 176 (b) 88 (c) 89 (d) 13
  29. 29.What is the 19th term of the AP 10, 13, 16, 19, …? (a) 64 (b) 57 (c) 54 (d) 67
  30. 30.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 192 (b) 96 (c) 108 (d) 26
  31. 31.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 420 (b) 390 (c) 780 (d) 60
  32. 32.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4851 (c) 4951 (d) 9900
  33. 33.What is the 39th term of the AP 6, 9, 12, 15, …? (a) 117 (b) 114 (c) 120 (d) 123
  34. 34.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 1432 (c) 1378 (d) 2862
  35. 35.Which term of the AP 14, 17, 20, 23, … is 107? (a) 31st (b) 32nd (c) 34th (d) 33rd
  36. 36.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 484 (b) 37 (c) 245 (d) 242
  37. 37.What is the missing term in the AP 19, 28, ?, 46, 55? (a) 38 (b) 37 (c) 36 (d) 46
  38. 38.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 22 (b) 23 (c) 21 (d) 20
  39. 39.What is the 20th term of the AP 6, 11, 16, 21, …? (a) 95 (b) 100 (c) 106 (d) 101
  40. 40.What is the 35th term of the AP 13, 18, 23, 28, …? (a) 188 (b) 183 (c) 175 (d) 170

Answer key

  1. 841
  2. 24
  3. 30
  4. 140
  5. 107
  6. 374
  7. 13
  8. 78
  9. 19th
  10. 196
  11. 112
  12. 25
  13. 4656
  14. 325
  15. 27th
  16. 4095
  17. 1176
  18. 24
  19. 216
  20. 27
  21. 35
  22. 23
  23. 528
  24. 100
  25. 25
  26. 90
  27. 80
  28. 88
  29. 64
  30. 96
  31. 390
  32. 4950
  33. 120
  34. 1431
  35. 32nd
  36. 242
  37. 37
  38. 21
  39. 101
  40. 183

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