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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 385 · 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 17, 26, ?, 44, 53? (a) 34 (b) 35 (c) 44 (d) 36
  2. 2.What is the 13th term of the AP 4, 8, 12, 16, …? (a) 56 (b) 53 (c) 48 (d) 52
  3. 3.What is the 13th term of the AP 6, 9, 12, 15, …? (a) 45 (b) 39 (c) 36 (d) 42
  4. 4.What is the 28th term of the AP 9, 11, 13, 15, …? (a) 63 (b) 65 (c) 56 (d) 54
  5. 5.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 19 (b) 20 (c) 21 (d) 24
  6. 6.What is the 34th term of the AP 18, 27, 36, 45, …? (a) 297 (b) 324 (c) 306 (d) 315
  7. 7.Which term of the AP 15, 18, 21, 24, … is 42? (a) 9th (b) 11th (c) 14th (d) 10th
  8. 8.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 1152 (c) 2352 (d) 1128
  9. 9.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 506 (d) 253
  10. 10.Which term of the AP 20, 26, 32, 38, … is 80? (a) 10th (b) 11th (c) 12th (d) 13th
  11. 11.What is the 13th term of the AP 19, 22, 25, 28, …? (a) 39 (b) 36 (c) 55 (d) 58
  12. 12.What is the 40th term of the AP 2, 8, 14, 20, …? (a) 242 (b) 240 (c) 236 (d) 234
  13. 13.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 63 (b) 64 (c) 11 (d) 126
  14. 14.What is the 12th term of the AP 1, 3, 5, 7, …? (a) 24 (b) 25 (c) 23 (d) 22
  15. 15.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 190 (c) 95 (d) 110
  16. 16.What is the 39th term of the AP 5, 11, 17, 23, …? (a) 234 (b) 239 (c) 233 (d) 228
  17. 17.What is the 38th term of the AP 17, 20, 23, 26, …? (a) 111 (b) 131 (c) 114 (d) 128
  18. 18.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4656 (d) 4608
  19. 19.Which term of the AP 20, 23, 26, 29, … is 59? (a) 13th (b) 15th (c) 14th (d) 16th
  20. 20.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 792 (b) 66 (c) 429 (d) 396
  21. 21.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 1806 (c) 861 (d) 903
  22. 22.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 24 (b) 26 (c) 25 (d) 30
  23. 23.What is the 29th term of the AP 4, 6, 8, 10, …? (a) 56 (b) 58 (c) 62 (d) 60
  24. 24.What is the 40th term of the AP 12, 17, 22, 27, …? (a) 195 (b) 212 (c) 207 (d) 200
  25. 25.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 75 (b) 65 (c) 21 (d) 130
  26. 26.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 65 (b) 130 (c) 19 (d) 68
  27. 27.Which term of the AP 19, 23, 27, 31, … is 91? (a) 21st (b) 19th (c) 20th (d) 18th
  28. 28.What is the missing term in the AP 20, 28, 36, ?, 52? (a) 45 (b) 44 (c) 43 (d) 52
  29. 29.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 8 (b) 9 (c) 10 (d) 15
  30. 30.What is the 15th term of the AP 3, 10, 17, 24, …? (a) 98 (b) 101 (c) 108 (d) 105
  31. 31.Which term of the AP 18, 21, 24, 27, … is 51? (a) 12th (b) 17th (c) 11th (d) 13th
  32. 32.Which term of the AP 18, 25, 32, 39, … is 270? (a) 39th (b) 36th (c) 38th (d) 37th
  33. 33.What is the 29th term of the AP 5, 8, 11, 14, …? (a) 89 (b) 92 (c) 84 (d) 87
  34. 34.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 33 (b) 24 (c) 26 (d) 25
  35. 35.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  36. 36.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 18 (b) 19 (c) 20 (d) 26
  37. 37.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 154 (d) 306
  38. 38.What is the 26th term of the AP 5, 7, 9, 11, …? (a) 52 (b) 50 (c) 57 (d) 55
  39. 39.What is the 39th term of the AP 12, 14, 16, 18, …? (a) 88 (b) 78 (c) 90 (d) 76
  40. 40.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 29 (d) 225

Answer key

  1. 35
  2. 52
  3. 42
  4. 63
  5. 20
  6. 315
  7. 10th
  8. 1176
  9. 484
  10. 11th
  11. 55
  12. 236
  13. 63
  14. 23
  15. 95
  16. 233
  17. 128
  18. 4656
  19. 14th
  20. 396
  21. 903
  22. 25
  23. 60
  24. 207
  25. 65
  26. 65
  27. 19th
  28. 44
  29. 9
  30. 101
  31. 12th
  32. 37th
  33. 89
  34. 25
  35. 64
  36. 19
  37. 153
  38. 55
  39. 88
  40. 225

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