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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 808 · 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 32? (a) 1056 (b) 496 (c) 512 (d) 528
  2. 2.What is the 38th term of the AP 5, 9, 13, 17, …? (a) 152 (b) 148 (c) 153 (d) 157
  3. 3.Which term of the AP 7, 13, 19, 25, … is 217? (a) 38th (b) 36th (c) 37th (d) 35th
  4. 4.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 21 (b) 29 (c) 20 (d) 22
  5. 5.Which term of the AP 6, 9, 12, 15, … is 36? (a) 11th (b) 13th (c) 10th (d) 12th
  6. 6.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 45 (c) 12 (d) 40
  7. 7.What is the 30th term of the AP 8, 10, 12, 14, …? (a) 68 (b) 60 (c) 66 (d) 58
  8. 8.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 648 (b) 49 (c) 324 (d) 348
  9. 9.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 344 (b) 192 (c) 172 (d) 39
  10. 10.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 418 (b) 34 (c) 212 (d) 209
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 484 (d) 43
  12. 12.What is the 12th term of the AP 14, 19, 24, 29, …? (a) 55 (b) 60 (c) 69 (d) 74
  13. 13.What is the 15th term of the AP 10, 13, 16, 19, …? (a) 45 (b) 42 (c) 55 (d) 52
  14. 14.Which term of the AP 14, 20, 26, 32, … is 242? (a) 38th (b) 41st (c) 40th (d) 39th
  15. 15.What is the 33rd term of the AP 19, 28, 37, 46, …? (a) 316 (b) 288 (c) 297 (d) 307
  16. 16.What is the 16th term of the AP 11, 20, 29, 38, …? (a) 144 (b) 135 (c) 155 (d) 146
  17. 17.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 30 (b) 35 (c) 28 (d) 29
  18. 18.What is the 16th term of the AP 7, 15, 23, 31, …? (a) 128 (b) 135 (c) 127 (d) 120
  19. 19.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 24 (b) 23 (c) 22 (d) 29
  20. 20.What is the 17th term of the AP 13, 21, 29, 37, …? (a) 141 (b) 136 (c) 128 (d) 149
  21. 21.Which term of the AP 2, 11, 20, 29, … is 74? (a) 8th (b) 9th (c) 11th (d) 10th
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  23. 23.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 13 (b) 14 (c) 19 (d) 12
  24. 24.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 15 (b) 18 (c) 16 (d) 14
  25. 25.What is the 20th term of the AP 14, 23, 32, 41, …? (a) 180 (b) 194 (c) 185 (d) 171
  26. 26.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 15 (c) 126 (d) 70
  27. 27.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 160 (b) 28 (c) 145 (d) 290
  28. 28.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 40 (b) 10 (c) 80 (d) 41
  29. 29.What is the 11th term of the AP 11, 13, 15, 17, …? (a) 20 (b) 33 (c) 22 (d) 31
  30. 30.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 756 (d) 729
  31. 31.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 90 (c) 180 (d) 91
  32. 32.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 8 (b) 11 (c) 10 (d) 9
  33. 33.What is the 30th term of the AP 6, 8, 10, 12, …? (a) 66 (b) 58 (c) 60 (d) 64
  34. 34.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 572 (b) 46 (c) 308 (d) 286
  35. 35.Which term of the AP 8, 14, 20, 26, … is 164? (a) 29th (b) 27th (c) 28th (d) 26th
  36. 36.What is the 21st term of the AP 3, 5, 7, 9, …? (a) 45 (b) 40 (c) 42 (d) 43
  37. 37.What is the 40th term of the AP 12, 20, 28, 36, …? (a) 320 (b) 312 (c) 324 (d) 332
  38. 38.Which term of the AP 11, 18, 25, 32, … is 186? (a) 26th (b) 25th (c) 28th (d) 27th
  39. 39.Which term of the AP 15, 20, 25, 30, … is 125? (a) 24th (b) 22nd (c) 25th (d) 23rd
  40. 40.What is the 17th term of the AP 14, 17, 20, 23, …? (a) 51 (b) 65 (c) 48 (d) 62

Answer key

  1. 528
  2. 153
  3. 36th
  4. 21
  5. 11th
  6. 40
  7. 66
  8. 324
  9. 172
  10. 209
  11. 484
  12. 69
  13. 52
  14. 39th
  15. 307
  16. 146
  17. 29
  18. 127
  19. 23
  20. 141
  21. 9th
  22. 36
  23. 13
  24. 15
  25. 185
  26. 63
  27. 145
  28. 40
  29. 31
  30. 729
  31. 90
  32. 9
  33. 64
  34. 286
  35. 27th
  36. 43
  37. 324
  38. 26th
  39. 23rd
  40. 62

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