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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 731 · 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 missing term in the AP 18, 22, 26, ?, 34? (a) 31 (b) 29 (c) 30 (d) 34
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  4. 4.What is the 34th term of the AP 9, 15, 21, 27, …? (a) 213 (b) 204 (c) 198 (d) 207
  5. 5.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 320 (b) 170 (c) 25 (d) 160
  6. 6.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 516 (b) 960 (c) 480 (d) 73
  7. 7.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 6 (b) 4 (c) 5 (d) 3
  8. 8.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 430 (b) 215 (c) 230 (d) 35
  9. 9.Which term of the AP 11, 13, 15, 17, … is 87? (a) 40th (b) 41st (c) 39th (d) 38th
  10. 10.What is the 38th term of the AP 7, 10, 13, 16, …? (a) 114 (b) 118 (c) 111 (d) 121
  11. 11.Which term of the AP 15, 18, 21, 24, … is 96? (a) 27th (b) 28th (c) 29th (d) 32nd
  12. 12.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 436 (c) 406 (d) 435
  13. 13.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 60 (b) 120 (c) 65 (d) 22
  14. 14.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 13 (b) 90 (c) 96 (d) 180
  15. 15.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 1122 (c) 561 (d) 528
  16. 16.What is the 33rd term of the AP 4, 13, 22, 31, …? (a) 292 (b) 301 (c) 288 (d) 297
  17. 17.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 29 (b) 24 (c) 22 (d) 23
  18. 18.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 78 (b) 19 (c) 69 (d) 138
  19. 19.What is the 23rd term of the AP 4, 6, 8, 10, …? (a) 50 (b) 48 (c) 46 (d) 44
  20. 20.Which term of the AP 1, 6, 11, 16, … is 136? (a) 30th (b) 27th (c) 29th (d) 28th
  21. 21.What is the 25th term of the AP 19, 21, 23, 25, …? (a) 69 (b) 50 (c) 48 (d) 67
  22. 22.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 162 (b) 171 (c) 26 (d) 324
  23. 23.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 288 (b) 576 (c) 315 (d) 56
  24. 24.Which term of the AP 6, 15, 24, 33, … is 339? (a) 39th (b) 40th (c) 37th (d) 38th
  25. 25.What is the 36th term of the AP 6, 10, 14, 18, …? (a) 146 (b) 144 (c) 140 (d) 150
  26. 26.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 67 (b) 814 (c) 440 (d) 407
  27. 27.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  28. 28.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 36 (b) 234 (c) 468 (d) 252
  29. 29.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 378 (b) 194 (c) 41 (d) 189
  30. 30.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 153 (c) 171 (d) 342
  31. 31.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 8 (b) 36 (c) 40 (d) 72
  32. 32.Which term of the AP 15, 24, 33, 42, … is 150? (a) 17th (b) 18th (c) 16th (d) 15th
  33. 33.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 169 (d) 91
  34. 34.What is the 18th term of the AP 3, 11, 19, 27, …? (a) 136 (b) 147 (c) 144 (d) 139
  35. 35.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 50 (b) 18 (c) 100 (d) 60
  36. 36.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 13 (b) 38 (c) 70 (d) 35
  37. 37.What is the 11th term of the AP 5, 10, 15, 20, …? (a) 60 (b) 55 (c) 56 (d) 50
  38. 38.Which term of the AP 12, 19, 26, 33, … is 117? (a) 16th (b) 18th (c) 15th (d) 17th
  39. 39.What is the 27th term of the AP 11, 18, 25, 32, …? (a) 189 (b) 182 (c) 193 (d) 200
  40. 40.What is the 13th term of the AP 8, 15, 22, 29, …? (a) 91 (b) 92 (c) 99 (d) 84

Answer key

  1. 30
  2. 100
  3. 49
  4. 207
  5. 160
  6. 480
  7. 4
  8. 215
  9. 39th
  10. 118
  11. 28th
  12. 435
  13. 60
  14. 90
  15. 561
  16. 292
  17. 23
  18. 69
  19. 48
  20. 28th
  21. 67
  22. 162
  23. 288
  24. 38th
  25. 146
  26. 407
  27. 784
  28. 234
  29. 189
  30. 171
  31. 36
  32. 16th
  33. 169
  34. 139
  35. 50
  36. 35
  37. 55
  38. 16th
  39. 193
  40. 92

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