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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 254 · 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, 8, 10, 12, … is 30? (a) 12th (b) 13th (c) 15th (d) 14th
  2. 2.What is the 19th term of the AP 2, 5, 8, 11, …? (a) 59 (b) 57 (c) 54 (d) 56
  3. 3.What is the 18th term of the AP 5, 13, 21, 29, …? (a) 141 (b) 144 (c) 136 (d) 149
  4. 4.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 38 (b) 40 (c) 48 (d) 39
  5. 5.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 4556 (d) 2278
  6. 6.Which term of the AP 6, 13, 20, 27, … is 55? (a) 9th (b) 7th (c) 10th (d) 8th
  7. 7.What is the 30th term of the AP 14, 17, 20, 23, …? (a) 87 (b) 104 (c) 90 (d) 101
  8. 8.What is the 26th term of the AP 18, 27, 36, 45, …? (a) 225 (b) 252 (c) 243 (d) 234
  9. 9.What is the 18th term of the AP 19, 23, 27, 31, …? (a) 91 (b) 68 (c) 87 (d) 72
  10. 10.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 504 (c) 252 (d) 48
  11. 11.Which term of the AP 9, 16, 23, 30, … is 226? (a) 31st (b) 33rd (c) 32nd (d) 34th
  12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  13. 13.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 300 (c) 326 (d) 325
  14. 14.Which term of the AP 14, 19, 24, 29, … is 129? (a) 25th (b) 24th (c) 23rd (d) 26th
  15. 15.What is the 20th term of the AP 16, 22, 28, 34, …? (a) 130 (b) 136 (c) 114 (d) 120
  16. 16.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 702 (d) 676
  17. 17.What is the 11th term of the AP 11, 20, 29, 38, …? (a) 110 (b) 101 (c) 99 (d) 90
  18. 18.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 930 (c) 465 (d) 59
  19. 19.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 300 (c) 288 (d) 600
  20. 20.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 100 (d) 19
  21. 21.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 40 (b) 6 (c) 20 (d) 21
  22. 22.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 4830 (c) 2415 (d) 2416
  23. 23.Which term of the AP 16, 20, 24, 28, … is 144? (a) 36th (b) 33rd (c) 34th (d) 32nd
  24. 24.What is the 39th term of the AP 2, 7, 12, 17, …? (a) 192 (b) 190 (c) 197 (d) 195
  25. 25.What is the 14th term of the AP 3, 9, 15, 21, …? (a) 81 (b) 87 (c) 78 (d) 84
  26. 26.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 25 (b) 29 (c) 26 (d) 27
  27. 27.What is the 33rd term of the AP 17, 24, 31, 38, …? (a) 241 (b) 224 (c) 231 (d) 248
  28. 28.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3321 (c) 3403 (d) 6806
  29. 29.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 19 (b) 104 (c) 192 (d) 96
  30. 30.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 132 (b) 120 (c) 240 (d) 30
  31. 31.What is the 33rd term of the AP 20, 24, 28, 32, …? (a) 132 (b) 148 (c) 128 (d) 152
  32. 32.What is the 40th term of the AP 2, 6, 10, 14, …? (a) 156 (b) 158 (c) 162 (d) 160
  33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 49 (d) 13
  34. 34.What is the missing term in the AP 12, 17, ?, 27, 32? (a) 21 (b) 22 (c) 23 (d) 27
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 306 (d) 153
  36. 36.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 15 (b) 12 (c) 11 (d) 13
  37. 37.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 13 (b) 17 (c) 15 (d) 14
  38. 38.What is the 32nd term of the AP 16, 19, 22, 25, …? (a) 112 (b) 96 (c) 109 (d) 93
  39. 39.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 76 (b) 516 (c) 1032 (d) 552
  40. 40.What is the 10th term of the AP 11, 19, 27, 35, …? (a) 72 (b) 83 (c) 80 (d) 91

Answer key

  1. 13th
  2. 56
  3. 141
  4. 39
  5. 2278
  6. 8th
  7. 101
  8. 243
  9. 87
  10. 252
  11. 32nd
  12. 121
  13. 325
  14. 24th
  15. 130
  16. 676
  17. 101
  18. 900
  19. 300
  20. 100
  21. 20
  22. 2415
  23. 33rd
  24. 192
  25. 81
  26. 26
  27. 241
  28. 3403
  29. 96
  30. 120
  31. 148
  32. 158
  33. 49
  34. 22
  35. 289
  36. 12
  37. 14
  38. 109
  39. 516
  40. 83

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