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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 682 · 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 58? (a) 1711 (b) 1682 (c) 3422 (d) 1653
  2. 2.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 84 (b) 104 (c) 88 (d) 100
  3. 3.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2211 (c) 4422 (d) 2145
  4. 4.Which term of the AP 19, 26, 33, 40, … is 124? (a) 15th (b) 17th (c) 18th (d) 16th
  5. 5.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 84 (b) 87 (c) 21 (d) 168
  6. 6.What is the 35th term of the AP 10, 19, 28, 37, …? (a) 315 (b) 306 (c) 316 (d) 325
  7. 7.What is the 29th term of the AP 16, 21, 26, 31, …? (a) 161 (b) 140 (c) 156 (d) 145
  8. 8.What is the 31st term of the AP 12, 21, 30, 39, …? (a) 279 (b) 282 (c) 270 (d) 291
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  10. 10.Which term of the AP 12, 18, 24, 30, … is 72? (a) 11th (b) 13th (c) 10th (d) 12th
  11. 11.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 232 (b) 47 (c) 416 (d) 208
  12. 12.What is the 23rd term of the AP 19, 26, 33, 40, …? (a) 154 (b) 161 (c) 180 (d) 173
  13. 13.What is the 24th term of the AP 3, 5, 7, 9, …? (a) 46 (b) 48 (c) 51 (d) 49
  14. 14.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 3160 (c) 3200 (d) 6480
  15. 15.What is the 13th term of the AP 3, 5, 7, 9, …? (a) 29 (b) 26 (c) 24 (d) 27
  16. 16.What is the missing term in the AP 18, ?, 28, 33, 38? (a) 28 (b) 23 (c) 24 (d) 22
  17. 17.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 73 (b) 140 (c) 19 (d) 70
  18. 18.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 171 (b) 342 (c) 35 (d) 189
  19. 19.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 45 (c) 13 (d) 50
  20. 20.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 75 (b) 130 (c) 21 (d) 65
  21. 21.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 217 (b) 46 (c) 196 (d) 392
  22. 22.What is the 11th term of the AP 15, 21, 27, 33, …? (a) 66 (b) 75 (c) 81 (d) 60
  23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 64 (d) 36
  24. 24.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 330 (b) 305 (c) 610 (d) 53
  25. 25.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 27 (b) 28 (c) 36 (d) 26
  26. 26.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 98 (b) 26 (c) 112 (d) 196
  27. 27.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 260 (c) 470 (d) 235
  28. 28.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 484 (b) 42 (c) 242 (d) 264
  29. 29.What is the 35th term of the AP 1, 4, 7, 10, …? (a) 105 (b) 102 (c) 103 (d) 106
  30. 30.What is the 33rd term of the AP 9, 12, 15, 18, …? (a) 96 (b) 105 (c) 108 (d) 99
  31. 31.Which term of the AP 17, 19, 21, 23, … is 73? (a) 30th (b) 28th (c) 29th (d) 31st
  32. 32.What is the 11th term of the AP 20, 29, 38, 47, …? (a) 90 (b) 119 (c) 99 (d) 110
  33. 33.Which term of the AP 10, 15, 20, 25, … is 105? (a) 19th (b) 21st (c) 20th (d) 22nd
  34. 34.What is the 15th term of the AP 16, 25, 34, 43, …? (a) 135 (b) 151 (c) 126 (d) 142
  35. 35.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 13 (b) 14 (c) 12 (d) 11
  36. 36.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 7832 (d) 3916
  37. 37.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 56 (b) 29 (c) 28 (d) 7
  38. 38.What is the 34th term of the AP 9, 14, 19, 24, …? (a) 165 (b) 174 (c) 179 (d) 170
  39. 39.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 47 (c) 319 (d) 297
  40. 40.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1485 (c) 3080 (d) 1540

Answer key

  1. 1711
  2. 100
  3. 2211
  4. 16th
  5. 84
  6. 316
  7. 156
  8. 282
  9. 25
  10. 11th
  11. 208
  12. 173
  13. 49
  14. 3240
  15. 27
  16. 23
  17. 70
  18. 171
  19. 45
  20. 65
  21. 196
  22. 75
  23. 64
  24. 305
  25. 27
  26. 98
  27. 235
  28. 242
  29. 103
  30. 105
  31. 29th
  32. 110
  33. 20th
  34. 142
  35. 12
  36. 3916
  37. 28
  38. 174
  39. 297
  40. 1540

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