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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 292 · 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.Which term of the AP 13, 22, 31, 40, … is 364? (a) 41st (b) 42nd (c) 39th (d) 40th
  2. 2.What is the 17th term of the AP 10, 13, 16, 19, …? (a) 61 (b) 58 (c) 51 (d) 48
  3. 3.What is the 34th term of the AP 11, 18, 25, 32, …? (a) 231 (b) 242 (c) 249 (d) 238
  4. 4.Which term of the AP 7, 10, 13, 16, … is 106? (a) 34th (b) 35th (c) 36th (d) 33rd
  5. 5.What is the 12th term of the AP 16, 19, 22, 25, …? (a) 33 (b) 52 (c) 36 (d) 49
  6. 6.What is the 24th term of the AP 2, 7, 12, 17, …? (a) 115 (b) 117 (c) 120 (d) 122
  7. 7.What is the missing term in the AP 8, 15, ?, 29, 36? (a) 23 (b) 29 (c) 21 (d) 22
  8. 8.What is the 38th term of the AP 16, 23, 30, 37, …? (a) 282 (b) 266 (c) 275 (d) 259
  9. 9.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 27 (b) 32 (c) 25 (d) 26
  10. 10.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 14 (b) 16 (c) 15 (d) 18
  11. 11.What is the 19th term of the AP 20, 22, 24, 26, …? (a) 38 (b) 58 (c) 36 (d) 56
  12. 12.What is the 27th term of the AP 15, 24, 33, 42, …? (a) 258 (b) 249 (c) 243 (d) 234
  13. 13.Which term of the AP 4, 11, 18, 25, … is 123? (a) 17th (b) 20th (c) 19th (d) 18th
  14. 14.Which term of the AP 19, 22, 25, 28, … is 127? (a) 39th (b) 37th (c) 38th (d) 36th
  15. 15.What is the 28th term of the AP 12, 16, 20, 24, …? (a) 108 (b) 112 (c) 120 (d) 124
  16. 16.What is the 37th term of the AP 16, 20, 24, 28, …? (a) 144 (b) 160 (c) 164 (d) 148
  17. 17.What is the 38th term of the AP 3, 8, 13, 18, …? (a) 185 (b) 188 (c) 193 (d) 190
  18. 18.What is the 27th term of the AP 8, 17, 26, 35, …? (a) 234 (b) 242 (c) 251 (d) 243
  19. 19.What is the 22nd term of the AP 14, 18, 22, 26, …? (a) 88 (b) 102 (c) 98 (d) 84
  20. 20.What is the 13th term of the AP 15, 24, 33, 42, …? (a) 123 (b) 108 (c) 132 (d) 117
  21. 21.What is the 24th term of the AP 3, 10, 17, 24, …? (a) 171 (b) 164 (c) 161 (d) 168
  22. 22.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 60 (b) 420 (c) 780 (d) 390
  23. 23.What is the 28th term of the AP 18, 27, 36, 45, …? (a) 243 (b) 261 (c) 252 (d) 270
  24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 25 (d) 91
  25. 25.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 32 (b) 370 (c) 200 (d) 185
  26. 26.Which term of the AP 20, 29, 38, 47, … is 128? (a) 12th (b) 14th (c) 15th (d) 13th
  27. 27.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 13 (b) 89 (c) 88 (d) 176
  28. 28.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 14 (b) 138 (c) 72 (d) 69
  29. 29.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 81 (b) 17 (c) 162 (d) 90
  30. 30.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1352 (c) 1326 (d) 1378
  31. 31.What is the 15th term of the AP 16, 23, 30, 37, …? (a) 121 (b) 105 (c) 114 (d) 98
  32. 32.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 119 (b) 112 (c) 22 (d) 224
  33. 33.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 84 (b) 88 (c) 168 (d) 14
  34. 34.What is the 35th term of the AP 14, 20, 26, 32, …? (a) 218 (b) 224 (c) 210 (d) 204
  35. 35.What is the 13th term of the AP 18, 21, 24, 27, …? (a) 39 (b) 54 (c) 36 (d) 57
  36. 36.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 595 (c) 1260 (d) 630
  37. 37.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 190 (c) 420 (d) 200
  38. 38.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 270 (b) 35 (c) 135 (d) 150
  39. 39.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 25 (b) 26 (c) 34 (d) 24
  40. 40.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 8010 (c) 4005 (d) 3916

Answer key

  1. 40th
  2. 58
  3. 242
  4. 34th
  5. 49
  6. 117
  7. 22
  8. 275
  9. 26
  10. 15
  11. 56
  12. 249
  13. 18th
  14. 37th
  15. 120
  16. 160
  17. 188
  18. 242
  19. 98
  20. 123
  21. 164
  22. 390
  23. 261
  24. 169
  25. 185
  26. 13th
  27. 88
  28. 69
  29. 81
  30. 1378
  31. 114
  32. 112
  33. 84
  34. 218
  35. 54
  36. 630
  37. 210
  38. 135
  39. 25
  40. 4005

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