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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 184 · 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 39th term of the AP 1, 7, 13, 19, …? (a) 234 (b) 235 (c) 228 (d) 229
  2. 2.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 804 (b) 61 (c) 402 (d) 432
  3. 3.What is the 16th term of the AP 1, 3, 5, 7, …? (a) 32 (b) 33 (c) 31 (d) 30
  4. 4.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 63 (c) 11 (d) 64
  5. 5.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 21 (c) 132 (d) 121
  6. 6.Which term of the AP 4, 12, 20, 28, … is 180? (a) 24th (b) 22nd (c) 23rd (d) 25th
  7. 7.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 324 (b) 19 (c) 168 (d) 162
  8. 8.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
  9. 9.What is the 28th term of the AP 4, 10, 16, 22, …? (a) 168 (b) 162 (c) 172 (d) 166
  10. 10.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  11. 11.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 24 (b) 27 (c) 25 (d) 23
  12. 12.Which term of the AP 20, 29, 38, 47, … is 182? (a) 18th (b) 20th (c) 19th (d) 21st
  13. 13.What is the 24th term of the AP 2, 10, 18, 26, …? (a) 186 (b) 192 (c) 184 (d) 194
  14. 14.What is the 39th term of the AP 9, 18, 27, 36, …? (a) 360 (b) 351 (c) 352 (d) 342
  15. 15.Which term of the AP 9, 16, 23, 30, … is 93? (a) 14th (b) 12th (c) 15th (d) 13th
  16. 16.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 11 (b) 13 (c) 12 (d) 18
  17. 17.Which term of the AP 14, 21, 28, 35, … is 189? (a) 27th (b) 28th (c) 25th (d) 26th
  18. 18.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1953 (c) 1891 (d) 3906
  19. 19.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 16 (b) 15 (c) 14 (d) 21
  20. 20.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 117 (b) 234 (c) 17 (d) 118
  21. 21.Which term of the AP 17, 20, 23, 26, … is 113? (a) 32nd (b) 34th (c) 35th (d) 33rd
  22. 22.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 14 (b) 12 (c) 15 (d) 13
  23. 23.Which term of the AP 5, 14, 23, 32, … is 266? (a) 29th (b) 31st (c) 30th (d) 32nd
  24. 24.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3042 (d) 3081
  25. 25.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 4970 (c) 2450 (d) 2415
  26. 26.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 1032 (b) 76 (c) 552 (d) 516
  27. 27.What is the 24th term of the AP 7, 9, 11, 13, …? (a) 48 (b) 53 (c) 46 (d) 55
  28. 28.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 16 (b) 17 (c) 18 (d) 19
  29. 29.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 780 (c) 741 (d) 1560
  30. 30.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 30 (b) 32 (c) 38 (d) 31
  31. 31.Which term of the AP 4, 7, 10, 13, … is 28? (a) 8th (b) 9th (c) 11th (d) 10th
  32. 32.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 2550 (c) 1225 (d) 1250
  33. 33.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1770 (d) 1711
  34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  35. 35.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 15 (b) 22 (c) 16 (d) 14
  36. 36.What is the 27th term of the AP 4, 11, 18, 25, …? (a) 193 (b) 189 (c) 182 (d) 186
  37. 37.What is the 12th term of the AP 11, 15, 19, 23, …? (a) 48 (b) 59 (c) 44 (d) 55
  38. 38.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 21 (b) 23 (c) 24 (d) 22
  39. 39.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 55 (b) 10 (c) 60 (d) 110
  40. 40.What is the 18th term of the AP 11, 15, 19, 23, …? (a) 79 (b) 83 (c) 68 (d) 72

Answer key

  1. 229
  2. 402
  3. 31
  4. 63
  5. 121
  6. 23rd
  7. 162
  8. 841
  9. 166
  10. 784
  11. 24
  12. 19th
  13. 186
  14. 351
  15. 13th
  16. 12
  17. 26th
  18. 1953
  19. 15
  20. 117
  21. 33rd
  22. 13
  23. 30th
  24. 3081
  25. 2485
  26. 516
  27. 53
  28. 17
  29. 780
  30. 31
  31. 9th
  32. 1275
  33. 1770
  34. 361
  35. 15
  36. 186
  37. 55
  38. 22
  39. 55
  40. 79

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