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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 21 · 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 19? (a) 171 (b) 380 (c) 191 (d) 190
  2. 2.Which term of the AP 17, 19, 21, 23, … is 45? (a) 16th (b) 15th (c) 14th (d) 17th
  3. 3.What is the 37th term of the AP 10, 12, 14, 16, …? (a) 82 (b) 74 (c) 84 (d) 72
  4. 4.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4465 (c) 4371 (d) 8930
  5. 5.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 170 (b) 29 (c) 155 (d) 310
  6. 6.What is the 28th term of the AP 20, 25, 30, 35, …? (a) 155 (b) 140 (c) 160 (d) 135
  7. 7.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 36 (c) 11 (d) 72
  8. 8.What is the 35th term of the AP 16, 23, 30, 37, …? (a) 245 (b) 238 (c) 261 (d) 254
  9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 57 (d) 841
  10. 10.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 19 (b) 155 (c) 308 (d) 154
  11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 59 (c) 465 (d) 930
  12. 12.What is the 14th term of the AP 10, 13, 16, 19, …? (a) 39 (b) 49 (c) 52 (d) 42
  13. 13.Which term of the AP 4, 7, 10, 13, … is 58? (a) 20th (b) 21st (c) 18th (d) 19th
  14. 14.What is the 15th term of the AP 2, 7, 12, 17, …? (a) 70 (b) 75 (c) 77 (d) 72
  15. 15.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 248 (b) 243 (c) 47 (d) 486
  16. 16.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 37 (b) 43 (c) 36 (d) 38
  17. 17.Which term of the AP 7, 15, 23, 31, … is 271? (a) 33rd (b) 35th (c) 36th (d) 34th
  18. 18.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 242 (b) 42 (c) 484 (d) 264
  19. 19.Which term of the AP 19, 21, 23, 25, … is 63? (a) 24th (b) 22nd (c) 23rd (d) 25th
  20. 20.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 132 (c) 264 (d) 37
  21. 21.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 19 (b) 16 (c) 14 (d) 15
  22. 22.What is the 34th term of the AP 14, 19, 24, 29, …? (a) 179 (b) 184 (c) 170 (d) 165
  23. 23.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 828 (b) 62 (c) 444 (d) 414
  24. 24.What is the 28th term of the AP 4, 9, 14, 19, …? (a) 135 (b) 139 (c) 144 (d) 140
  25. 25.What is the 16th term of the AP 2, 4, 6, 8, …? (a) 34 (b) 32 (c) 33 (d) 30
  26. 26.What is the 18th term of the AP 1, 3, 5, 7, …? (a) 37 (b) 35 (c) 34 (d) 36
  27. 27.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 186 (b) 93 (c) 23 (d) 102
  28. 28.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 3540 (c) 1771 (d) 1711
  29. 29.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 78 (d) 23
  30. 30.Which term of the AP 12, 18, 24, 30, … is 150? (a) 26th (b) 24th (c) 23rd (d) 25th
  31. 31.What is the 25th term of the AP 16, 25, 34, 43, …? (a) 225 (b) 216 (c) 241 (d) 232
  32. 32.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 35 (c) 70 (d) 40
  33. 33.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 7 (b) 11 (c) 5 (d) 6
  34. 34.What is the 11th term of the AP 2, 4, 6, 8, …? (a) 23 (b) 24 (c) 20 (d) 22
  35. 35.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 110 (b) 105 (c) 210 (d) 15
  36. 36.What is the 15th term of the AP 11, 20, 29, 38, …? (a) 146 (b) 135 (c) 126 (d) 137
  37. 37.Which term of the AP 15, 17, 19, 21, … is 81? (a) 33rd (b) 35th (c) 36th (d) 34th
  38. 38.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 35 (b) 36 (c) 8 (d) 70
  39. 39.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 126 (b) 21 (c) 117 (d) 234
  40. 40.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 36 (b) 462 (c) 231 (d) 234

Answer key

  1. 190
  2. 15th
  3. 82
  4. 4465
  5. 155
  6. 155
  7. 36
  8. 254
  9. 841
  10. 154
  11. 900
  12. 49
  13. 19th
  14. 72
  15. 243
  16. 37
  17. 34th
  18. 242
  19. 23rd
  20. 132
  21. 15
  22. 179
  23. 414
  24. 139
  25. 32
  26. 35
  27. 93
  28. 1770
  29. 144
  30. 24th
  31. 232
  32. 35
  33. 6
  34. 22
  35. 105
  36. 137
  37. 34th
  38. 35
  39. 117
  40. 231

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