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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 159 · 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 12 terms of the AP 6, 12, 18, …? (a) 504 (b) 936 (c) 468 (d) 72
  2. 2.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 7 (b) 10 (c) 6 (d) 8
  3. 3.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 676 (d) 351
  4. 4.What is the sum of all the whole numbers from 1 to 60? (a) 1830 (b) 3660 (c) 1770 (d) 1800
  5. 5.What is the 18th term of the AP 16, 22, 28, 34, …? (a) 108 (b) 118 (c) 124 (d) 102
  6. 6.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 57 (c) 870 (d) 435
  7. 7.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  8. 8.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 432 (b) 468 (c) 69 (d) 864
  9. 9.What is the 10th term of the AP 1, 9, 17, 25, …? (a) 72 (b) 73 (c) 81 (d) 80
  10. 10.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 84 (b) 20 (c) 75 (d) 150
  11. 11.What is the 17th term of the AP 9, 11, 13, 15, …? (a) 32 (b) 34 (c) 43 (d) 41
  12. 12.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
  13. 13.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 128 (b) 72 (c) 15 (d) 64
  14. 14.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 720 (b) 360 (c) 384 (d) 52
  15. 15.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 42 (b) 33 (c) 34 (d) 32
  16. 16.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 144 (b) 78 (c) 17 (d) 72
  17. 17.What is the 14th term of the AP 3, 12, 21, 30, …? (a) 129 (b) 117 (c) 126 (d) 120
  18. 18.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 21 (b) 23 (c) 30 (d) 22
  19. 19.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1226 (c) 1176 (d) 1225
  20. 20.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 140 (b) 70 (c) 16 (d) 77
  21. 21.What is the 17th term of the AP 9, 18, 27, 36, …? (a) 144 (b) 162 (c) 153 (d) 154
  22. 22.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 35 (b) 222 (c) 444 (d) 240
  23. 23.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 24 (c) 70 (d) 75
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  25. 25.What is the 32nd term of the AP 12, 21, 30, 39, …? (a) 288 (b) 291 (c) 279 (d) 300
  26. 26.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 17 (b) 10 (c) 9 (d) 11
  27. 27.What is the missing term in the AP 19, 28, 37, ?, 55? (a) 55 (b) 45 (c) 46 (d) 47
  28. 28.What is the 39th term of the AP 13, 18, 23, 28, …? (a) 203 (b) 208 (c) 195 (d) 190
  29. 29.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 435 (d) 930
  30. 30.What is the 23rd term of the AP 8, 16, 24, 32, …? (a) 185 (b) 184 (c) 192 (d) 176
  31. 31.What is the 33rd term of the AP 17, 19, 21, 23, …? (a) 81 (b) 64 (c) 66 (d) 83
  32. 32.What is the 16th term of the AP 10, 13, 16, 19, …? (a) 48 (b) 45 (c) 58 (d) 55
  33. 33.Which term of the AP 8, 11, 14, 17, … is 80? (a) 25th (b) 26th (c) 27th (d) 24th
  34. 34.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 180 (b) 30 (c) 330 (d) 165
  35. 35.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 22 (b) 21 (c) 20 (d) 26
  36. 36.What is the 37th term of the AP 18, 22, 26, 30, …? (a) 166 (b) 162 (c) 148 (d) 144
  37. 37.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 126 (c) 13 (d) 63
  38. 38.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 44 (b) 9 (c) 48 (d) 88
  39. 39.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 631 (c) 595 (d) 630
  40. 40.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 528 (b) 492 (c) 74 (d) 984

Answer key

  1. 468
  2. 7
  3. 676
  4. 1830
  5. 118
  6. 841
  7. 91
  8. 432
  9. 73
  10. 75
  11. 41
  12. 529
  13. 64
  14. 360
  15. 33
  16. 72
  17. 120
  18. 22
  19. 1225
  20. 70
  21. 153
  22. 222
  23. 70
  24. 100
  25. 291
  26. 10
  27. 46
  28. 203
  29. 465
  30. 184
  31. 81
  32. 55
  33. 25th
  34. 165
  35. 21
  36. 162
  37. 63
  38. 44
  39. 630
  40. 492

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