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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 531 · 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 25th term of the AP 12, 15, 18, 21, …? (a) 87 (b) 72 (c) 75 (d) 84
  2. 2.What is the 40th term of the AP 12, 16, 20, 24, …? (a) 160 (b) 156 (c) 168 (d) 172
  3. 3.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 56 (b) 372 (c) 684 (d) 342
  4. 4.What is the 26th term of the AP 8, 17, 26, 35, …? (a) 233 (b) 242 (c) 234 (d) 225
  5. 5.Which term of the AP 11, 13, 15, 17, … is 37? (a) 16th (b) 13th (c) 14th (d) 15th
  6. 6.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 562 (c) 1122 (d) 528
  7. 7.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 9 (b) 10 (c) 11 (d) 13
  8. 8.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 35 (b) 26 (c) 27 (d) 25
  9. 9.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 15 (b) 10 (c) 12 (d) 11
  10. 10.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 27 (c) 87 (d) 174
  11. 11.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  12. 12.What is the 20th term of the AP 6, 10, 14, 18, …? (a) 86 (b) 82 (c) 80 (d) 76
  13. 13.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 118 (b) 17 (c) 234 (d) 117
  14. 14.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 340 (b) 630 (c) 54 (d) 315
  15. 15.What is the 39th term of the AP 20, 26, 32, 38, …? (a) 254 (b) 234 (c) 228 (d) 248
  16. 16.What is the 11th term of the AP 13, 22, 31, 40, …? (a) 99 (b) 90 (c) 103 (d) 112
  17. 17.Which term of the AP 11, 17, 23, 29, … is 107? (a) 19th (b) 17th (c) 16th (d) 18th
  18. 18.What is the 18th term of the AP 19, 26, 33, 40, …? (a) 119 (b) 126 (c) 145 (d) 138
  19. 19.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 68 (c) 130 (d) 65
  20. 20.What is the 13th term of the AP 18, 24, 30, 36, …? (a) 72 (b) 78 (c) 96 (d) 90
  21. 21.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 67 (b) 66 (c) 11 (d) 132
  22. 22.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 138 (b) 69 (c) 14 (d) 72
  23. 23.What is the 10th term of the AP 4, 10, 16, 22, …? (a) 58 (b) 54 (c) 60 (d) 64
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  25. 25.What is the 13th term of the AP 14, 19, 24, 29, …? (a) 65 (b) 60 (c) 79 (d) 74
  26. 26.Which term of the AP 5, 8, 11, 14, … is 92? (a) 32nd (b) 29th (c) 31st (d) 30th
  27. 27.What is the 36th term of the AP 2, 11, 20, 29, …? (a) 326 (b) 317 (c) 315 (d) 324
  28. 28.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 53 (b) 288 (c) 522 (d) 261
  29. 29.What is the 11th term of the AP 18, 26, 34, 42, …? (a) 98 (b) 88 (c) 106 (d) 80
  30. 30.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 256 (d) 272
  31. 31.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 49 (d) 650
  32. 32.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 50 (c) 100 (d) 55
  33. 33.What is the 27th term of the AP 17, 19, 21, 23, …? (a) 71 (b) 52 (c) 54 (d) 69
  34. 34.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 46 (c) 11 (d) 45
  35. 35.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 21 (b) 17 (c) 18 (d) 19
  36. 36.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 225 (d) 120
  37. 37.What is the 38th term of the AP 4, 10, 16, 22, …? (a) 226 (b) 228 (c) 222 (d) 232
  38. 38.What is the 39th term of the AP 4, 8, 12, 16, …? (a) 152 (b) 157 (c) 160 (d) 156
  39. 39.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 15 (b) 17 (c) 19 (d) 16
  40. 40.What is the 17th term of the AP 15, 19, 23, 27, …? (a) 83 (b) 64 (c) 68 (d) 79

Answer key

  1. 84
  2. 168
  3. 342
  4. 233
  5. 14th
  6. 561
  7. 10
  8. 26
  9. 11
  10. 87
  11. 361
  12. 82
  13. 117
  14. 315
  15. 248
  16. 103
  17. 17th
  18. 138
  19. 65
  20. 90
  21. 66
  22. 69
  23. 58
  24. 100
  25. 74
  26. 30th
  27. 317
  28. 261
  29. 98
  30. 256
  31. 625
  32. 50
  33. 69
  34. 45
  35. 18
  36. 225
  37. 226
  38. 156
  39. 16
  40. 79

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