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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 346 · 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 6, 12, 18, 24, … is 150? (a) 24th (b) 27th (c) 25th (d) 26th
  2. 2.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 96 (c) 48 (d) 54
  3. 3.What is the 26th term of the AP 8, 14, 20, 26, …? (a) 150 (b) 164 (c) 156 (d) 158
  4. 4.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 9 (b) 19 (c) 10 (d) 11
  5. 5.What is the 16th term of the AP 7, 9, 11, 13, …? (a) 32 (b) 30 (c) 37 (d) 39
  6. 6.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 24 (c) 70 (d) 75
  7. 7.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 7 (b) 5 (c) 8 (d) 6
  8. 8.What is the 12th term of the AP 14, 18, 22, 26, …? (a) 62 (b) 58 (c) 48 (d) 44
  9. 9.What is the 32nd term of the AP 4, 13, 22, 31, …? (a) 283 (b) 292 (c) 279 (d) 288
  10. 10.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 40 (b) 180 (c) 200 (d) 360
  11. 11.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 78 (b) 156 (c) 12 (d) 84
  12. 12.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 28 (b) 26 (c) 24 (d) 25
  13. 13.What is the 23rd term of the AP 15, 22, 29, 36, …? (a) 154 (b) 161 (c) 169 (d) 176
  14. 14.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 18 (b) 26 (c) 20 (d) 19
  15. 15.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 125 (b) 130 (c) 250 (d) 17
  16. 16.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 27 (b) 25 (c) 29 (d) 26
  17. 17.What is the 21st term of the AP 15, 20, 25, 30, …? (a) 115 (b) 100 (c) 105 (d) 120
  18. 18.What is the 26th term of the AP 9, 17, 25, 33, …? (a) 217 (b) 208 (c) 209 (d) 200
  19. 19.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 14 (b) 9 (c) 10 (d) 11
  20. 20.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 7 (b) 28 (c) 56 (d) 29
  21. 21.Which term of the AP 16, 23, 30, 37, … is 240? (a) 33rd (b) 32nd (c) 35th (d) 34th
  22. 22.Which term of the AP 9, 14, 19, 24, … is 124? (a) 24th (b) 23rd (c) 26th (d) 25th
  23. 23.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 143 (c) 286 (d) 18
  24. 24.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 270 (b) 486 (c) 51 (d) 243
  25. 25.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 147 (b) 168 (c) 294 (d) 39
  26. 26.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 240 (b) 220 (c) 440 (d) 45
  27. 27.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 132 (b) 21 (c) 242 (d) 121
  28. 28.Which term of the AP 14, 17, 20, 23, … is 71? (a) 19th (b) 21st (c) 22nd (d) 20th
  29. 29.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 2652 (c) 1326 (d) 1275
  30. 30.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 232 (b) 128 (c) 116 (d) 25
  31. 31.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 132 (b) 21 (c) 66 (d) 78
  32. 32.What is the 18th term of the AP 3, 5, 7, 9, …? (a) 39 (b) 34 (c) 36 (d) 37
  33. 33.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 741 (c) 703 (d) 1482
  34. 34.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 336 (c) 168 (d) 39
  35. 35.Which term of the AP 14, 21, 28, 35, … is 84? (a) 11th (b) 12th (c) 10th (d) 13th
  36. 36.Which term of the AP 1, 10, 19, 28, … is 118? (a) 13th (b) 15th (c) 14th (d) 16th
  37. 37.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 30 (c) 210 (d) 105
  38. 38.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 242 (b) 484 (c) 37 (d) 245
  39. 39.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 748 (b) 374 (c) 64 (d) 407
  40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 21 (d) 66

Answer key

  1. 25th
  2. 48
  3. 158
  4. 10
  5. 37
  6. 70
  7. 6
  8. 58
  9. 283
  10. 180
  11. 78
  12. 25
  13. 169
  14. 19
  15. 125
  16. 26
  17. 115
  18. 209
  19. 10
  20. 28
  21. 33rd
  22. 24th
  23. 143
  24. 243
  25. 147
  26. 220
  27. 121
  28. 20th
  29. 1326
  30. 116
  31. 66
  32. 37
  33. 741
  34. 168
  35. 11th
  36. 14th
  37. 105
  38. 242
  39. 374
  40. 121

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