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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 741 · 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 the first 12 terms of the AP 1, 6, 11, …? (a) 342 (b) 372 (c) 684 (d) 56
  2. 2.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 340 (b) 620 (c) 58 (d) 310
  3. 3.What is the 10th term of the AP 14, 21, 28, 35, …? (a) 63 (b) 84 (c) 70 (d) 77
  4. 4.What is the 13th term of the AP 3, 5, 7, 9, …? (a) 26 (b) 29 (c) 27 (d) 24
  5. 5.What is the 26th term of the AP 12, 17, 22, 27, …? (a) 137 (b) 125 (c) 130 (d) 142
  6. 6.What is the 18th term of the AP 20, 26, 32, 38, …? (a) 128 (b) 108 (c) 102 (d) 122
  7. 7.What is the 26th term of the AP 10, 12, 14, 16, …? (a) 50 (b) 52 (c) 62 (d) 60
  8. 8.Which term of the AP 19, 22, 25, 28, … is 82? (a) 21st (b) 22nd (c) 23rd (d) 24th
  9. 9.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 312 (b) 576 (c) 288 (d) 46
  10. 10.What is the 16th term of the AP 8, 14, 20, 26, …? (a) 96 (b) 98 (c) 90 (d) 104
  11. 11.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 99 (c) 198 (d) 108
  12. 12.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 38 (b) 516 (c) 276 (d) 258
  13. 13.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 27 (b) 26 (c) 31 (d) 25
  14. 14.What is the 16th term of the AP 8, 17, 26, 35, …? (a) 135 (b) 144 (c) 143 (d) 152
  15. 15.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 14 (b) 72 (c) 69 (d) 138
  16. 16.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 31 (b) 40 (c) 32 (d) 30
  17. 17.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 105 (c) 98 (d) 210
  18. 18.What is the 11th term of the AP 11, 15, 19, 23, …? (a) 40 (b) 55 (c) 44 (d) 51
  19. 19.Which term of the AP 17, 23, 29, 35, … is 191? (a) 29th (b) 31st (c) 30th (d) 32nd
  20. 20.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 68 (b) 130 (c) 19 (d) 65
  21. 21.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 99 (b) 29 (c) 114 (d) 198
  22. 22.What is the 39th term of the AP 5, 14, 23, 32, …? (a) 347 (b) 356 (c) 342 (d) 351
  23. 23.Which term of the AP 10, 12, 14, 16, … is 64? (a) 29th (b) 32nd (c) 28th (d) 27th
  24. 24.What is the 35th term of the AP 5, 14, 23, 32, …? (a) 320 (b) 311 (c) 315 (d) 306
  25. 25.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 220 (b) 40 (c) 440 (d) 240
  26. 26.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 20 (b) 21 (c) 19 (d) 23
  27. 27.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 21 (b) 75 (c) 78 (d) 150
  28. 28.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 260 (b) 44 (c) 280 (d) 520
  29. 29.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 23 (b) 288 (c) 156 (d) 144
  30. 30.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 192 (b) 45 (c) 216 (d) 384
  31. 31.What is the 15th term of the AP 12, 16, 20, 24, …? (a) 72 (b) 56 (c) 60 (d) 68
  32. 32.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  33. 33.Which term of the AP 4, 13, 22, 31, … is 121? (a) 16th (b) 15th (c) 14th (d) 13th
  34. 34.What is the 18th term of the AP 15, 20, 25, 30, …? (a) 105 (b) 85 (c) 90 (d) 100
  35. 35.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 87 (b) 174 (c) 22 (d) 96
  36. 36.What is the 24th term of the AP 9, 13, 17, 21, …? (a) 96 (b) 105 (c) 101 (d) 92
  37. 37.Which term of the AP 2, 8, 14, 20, … is 134? (a) 22nd (b) 25th (c) 23rd (d) 24th
  38. 38.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 14 (b) 12 (c) 17 (d) 13
  39. 39.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 39 (c) 400 (d) 210
  40. 40.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 225 (c) 450 (d) 243

Answer key

  1. 342
  2. 310
  3. 77
  4. 27
  5. 137
  6. 122
  7. 60
  8. 22nd
  9. 288
  10. 98
  11. 99
  12. 258
  13. 26
  14. 143
  15. 69
  16. 31
  17. 105
  18. 51
  19. 30th
  20. 65
  21. 99
  22. 347
  23. 28th
  24. 311
  25. 220
  26. 20
  27. 75
  28. 260
  29. 144
  30. 192
  31. 68
  32. 100
  33. 14th
  34. 100
  35. 87
  36. 101
  37. 23rd
  38. 13
  39. 400
  40. 225

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