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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 168 · 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 30? (a) 435 (b) 930 (c) 465 (d) 450
  2. 2.What is the 15th term of the AP 8, 10, 12, 14, …? (a) 28 (b) 30 (c) 36 (d) 38
  3. 3.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100
  4. 4.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 21 (b) 23 (c) 22 (d) 27
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306
  6. 6.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 18 (b) 120 (c) 63 (d) 60
  7. 7.Which term of the AP 4, 13, 22, 31, … is 103? (a) 13th (b) 11th (c) 14th (d) 12th
  8. 8.Which term of the AP 8, 13, 18, 23, … is 123? (a) 23rd (b) 25th (c) 24th (d) 26th
  9. 9.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 54 (b) 51 (c) 11 (d) 102
  10. 10.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  11. 11.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 26 (b) 19 (c) 21 (d) 20
  12. 12.What is the 23rd term of the AP 18, 20, 22, 24, …? (a) 44 (b) 46 (c) 64 (d) 62
  13. 13.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 108 (c) 28 (d) 93
  14. 14.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 70 (b) 77 (c) 140 (d) 16
  15. 15.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 210 (b) 378 (c) 189 (d) 45
  16. 16.What is the 39th term of the AP 4, 11, 18, 25, …? (a) 270 (b) 277 (c) 273 (d) 266
  17. 17.Which term of the AP 5, 7, 9, 11, … is 57? (a) 26th (b) 28th (c) 27th (d) 29th
  18. 18.What is the 35th term of the AP 18, 26, 34, 42, …? (a) 290 (b) 272 (c) 280 (d) 298
  19. 19.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 682 (b) 56 (c) 346 (d) 341
  20. 20.What is the 29th term of the AP 15, 20, 25, 30, …? (a) 155 (b) 160 (c) 140 (d) 145
  21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
  22. 22.What is the 13th term of the AP 13, 17, 21, 25, …? (a) 65 (b) 61 (c) 48 (d) 52
  23. 23.What is the 27th term of the AP 9, 13, 17, 21, …? (a) 113 (b) 117 (c) 108 (d) 104
  24. 24.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 216 (b) 16 (c) 108 (d) 109
  25. 25.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 121 (c) 105 (d) 120
  26. 26.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 27 (b) 26 (c) 25 (d) 28
  27. 27.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 110 (b) 20 (c) 120 (d) 220
  28. 28.What is the 10th term of the AP 14, 20, 26, 32, …? (a) 74 (b) 60 (c) 54 (d) 68
  29. 29.What is the 17th term of the AP 11, 13, 15, 17, …? (a) 32 (b) 43 (c) 45 (d) 34
  30. 30.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 11 (b) 64 (c) 126 (d) 63
  31. 31.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 17 (b) 81 (c) 162 (d) 90
  32. 32.What is the 33rd term of the AP 17, 24, 31, 38, …? (a) 224 (b) 231 (c) 241 (d) 248
  33. 33.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2556 (c) 2485 (d) 5112
  34. 34.What is the 26th term of the AP 7, 15, 23, 31, …? (a) 207 (b) 208 (c) 215 (d) 200
  35. 35.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 171 (b) 306 (c) 153 (d) 33
  36. 36.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 19 (b) 26 (c) 17 (d) 18
  37. 37.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 30 (b) 36 (c) 29 (d) 31
  38. 38.What is the 12th term of the AP 15, 23, 31, 39, …? (a) 111 (b) 88 (c) 103 (d) 96
  39. 39.What is the 32nd term of the AP 5, 14, 23, 32, …? (a) 293 (b) 288 (c) 279 (d) 284
  40. 40.What is the 14th term of the AP 3, 10, 17, 24, …? (a) 94 (b) 101 (c) 98 (d) 91

Answer key

  1. 465
  2. 36
  3. 100
  4. 22
  5. 289
  6. 60
  7. 12th
  8. 24th
  9. 51
  10. 121
  11. 20
  12. 62
  13. 93
  14. 70
  15. 189
  16. 270
  17. 27th
  18. 290
  19. 341
  20. 155
  21. 676
  22. 61
  23. 113
  24. 108
  25. 120
  26. 26
  27. 110
  28. 68
  29. 43
  30. 63
  31. 81
  32. 241
  33. 2556
  34. 207
  35. 153
  36. 18
  37. 30
  38. 103
  39. 284
  40. 94

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