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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 639 · 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 missing term in the AP 9, 12, ?, 18, 21? (a) 16 (b) 15 (c) 18 (d) 14
  2. 2.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 462 (b) 231 (c) 41 (d) 253
  3. 3.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 190 (d) 200
  4. 4.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 576 (d) 300
  5. 5.What is the 24th term of the AP 7, 13, 19, 25, …? (a) 145 (b) 138 (c) 151 (d) 144
  6. 6.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 119 (b) 112 (c) 22 (d) 224
  7. 7.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 57 (b) 114 (c) 17 (d) 66
  8. 8.Which term of the AP 15, 19, 23, 27, … is 43? (a) 9th (b) 7th (c) 10th (d) 8th
  9. 9.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 196 (d) 210
  10. 10.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3003 (c) 6162 (d) 3081
  11. 11.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 194 (b) 378 (c) 41 (d) 189
  12. 12.What is the 21st term of the AP 20, 22, 24, 26, …? (a) 60 (b) 40 (c) 62 (d) 42
  13. 13.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 352 (b) 176 (c) 192 (d) 36
  14. 14.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 65 (b) 23 (c) 70 (d) 130
  15. 15.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 1056 (c) 528 (d) 496
  16. 16.What is the 36th term of the AP 4, 6, 8, 10, …? (a) 72 (b) 76 (c) 70 (d) 74
  17. 17.Which term of the AP 7, 13, 19, 25, … is 133? (a) 22nd (b) 24th (c) 21st (d) 23rd
  18. 18.What is the 38th term of the AP 7, 12, 17, 22, …? (a) 192 (b) 197 (c) 185 (d) 190
  19. 19.What is the 34th term of the AP 19, 21, 23, 25, …? (a) 87 (b) 68 (c) 85 (d) 66
  20. 20.What is the missing term in the AP 4, ?, 16, 22, 28? (a) 16 (b) 11 (c) 10 (d) 9
  21. 21.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 108 (c) 24 (d) 99
  22. 22.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 140 (b) 75 (c) 70 (d) 18
  23. 23.What is the 23rd term of the AP 19, 27, 35, 43, …? (a) 203 (b) 176 (c) 184 (d) 195
  24. 24.What is the 26th term of the AP 8, 12, 16, 20, …? (a) 108 (b) 104 (c) 100 (d) 112
  25. 25.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 40 (b) 39 (c) 48 (d) 38
  26. 26.What is the 38th term of the AP 2, 11, 20, 29, …? (a) 344 (b) 335 (c) 333 (d) 342
  27. 27.What is the 31st term of the AP 14, 17, 20, 23, …? (a) 107 (b) 90 (c) 104 (d) 93
  28. 28.What is the 16th term of the AP 18, 23, 28, 33, …? (a) 93 (b) 98 (c) 80 (d) 75
  29. 29.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 23 (b) 22 (c) 28 (d) 24
  30. 30.Which term of the AP 19, 21, 23, 25, … is 83? (a) 33rd (b) 32nd (c) 35th (d) 34th
  31. 31.What is the 15th term of the AP 3, 9, 15, 21, …? (a) 84 (b) 93 (c) 87 (d) 90
  32. 32.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
  33. 33.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 51 (b) 372 (c) 696 (d) 348
  34. 34.What is the 27th term of the AP 8, 17, 26, 35, …? (a) 242 (b) 251 (c) 243 (d) 234
  35. 35.What is the 34th term of the AP 15, 17, 19, 21, …? (a) 83 (b) 68 (c) 66 (d) 81
  36. 36.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 702 (d) 51
  37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 23 (d) 78
  38. 38.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 55 (c) 110 (d) 45
  39. 39.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 5402 (c) 2701 (d) 2702
  40. 40.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 408 (b) 59 (c) 378 (d) 756

Answer key

  1. 15
  2. 231
  3. 210
  4. 576
  5. 145
  6. 112
  7. 57
  8. 8th
  9. 196
  10. 3081
  11. 189
  12. 60
  13. 176
  14. 65
  15. 528
  16. 74
  17. 22nd
  18. 192
  19. 85
  20. 10
  21. 99
  22. 70
  23. 195
  24. 108
  25. 39
  26. 335
  27. 104
  28. 93
  29. 23
  30. 33rd
  31. 87
  32. 49
  33. 348
  34. 242
  35. 81
  36. 676
  37. 144
  38. 55
  39. 2701
  40. 378

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