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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 367 · 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 15th term of the AP 13, 16, 19, 22, …? (a) 55 (b) 45 (c) 42 (d) 58
  2. 2.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 100 (b) 198 (c) 99 (d) 15
  3. 3.Which term of the AP 14, 17, 20, 23, … is 125? (a) 38th (b) 37th (c) 39th (d) 40th
  4. 4.What is the 11th term of the AP 19, 21, 23, 25, …? (a) 39 (b) 20 (c) 22 (d) 41
  5. 5.What is the 14th term of the AP 2, 6, 10, 14, …? (a) 58 (b) 56 (c) 52 (d) 54
  6. 6.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 16 (b) 8 (c) 10 (d) 9
  7. 7.What is the 39th term of the AP 7, 16, 25, 34, …? (a) 342 (b) 349 (c) 358 (d) 351
  8. 8.What is the 31st term of the AP 13, 16, 19, 22, …? (a) 106 (b) 103 (c) 93 (d) 90
  9. 9.Which term of the AP 12, 14, 16, 18, … is 62? (a) 25th (b) 26th (c) 27th (d) 31st
  10. 10.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 192 (b) 176 (c) 36 (d) 352
  11. 11.Which term of the AP 10, 15, 20, 25, … is 150? (a) 30th (b) 29th (c) 31st (d) 28th
  12. 12.Which term of the AP 7, 11, 15, 19, … is 119? (a) 30th (b) 31st (c) 28th (d) 29th
  13. 13.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 180 (b) 330 (c) 165 (d) 30
  14. 14.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 153 (c) 136 (d) 306
  15. 15.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 240 (d) 120
  16. 16.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 27 (d) 105
  17. 17.What is the missing term in the AP 6, 12, ?, 24, 30? (a) 17 (b) 24 (c) 18 (d) 19
  18. 18.What is the 25th term of the AP 17, 19, 21, 23, …? (a) 48 (b) 67 (c) 50 (d) 65
  19. 19.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 121 (b) 242 (c) 122 (d) 16
  20. 20.What is the 14th term of the AP 14, 16, 18, 20, …? (a) 42 (b) 28 (c) 26 (d) 40
  21. 21.What is the 13th term of the AP 3, 5, 7, 9, …? (a) 24 (b) 26 (c) 29 (d) 27
  22. 22.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 2652 (c) 1327 (d) 1326
  23. 23.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 120 (b) 25 (c) 234 (d) 117
  24. 24.Which term of the AP 6, 15, 24, 33, … is 105? (a) 11th (b) 12th (c) 14th (d) 13th
  25. 25.What is the 15th term of the AP 10, 19, 28, 37, …? (a) 135 (b) 126 (c) 145 (d) 136
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 15 (d) 64
  27. 27.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 45 (d) 529
  28. 28.What is the 17th term of the AP 18, 22, 26, 30, …? (a) 82 (b) 68 (c) 86 (d) 64
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  30. 30.What is the 21st term of the AP 6, 9, 12, 15, …? (a) 60 (b) 66 (c) 63 (d) 69
  31. 31.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 242 (c) 506 (d) 253
  32. 32.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 676 (d) 351
  33. 33.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 180 (b) 14 (c) 91 (d) 90
  34. 34.What is the 13th term of the AP 16, 25, 34, 43, …? (a) 108 (b) 124 (c) 133 (d) 117
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  36. 36.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 21 (b) 20 (c) 19 (d) 22
  37. 37.Which term of the AP 20, 26, 32, 38, … is 140? (a) 23rd (b) 20th (c) 22nd (d) 21st
  38. 38.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 297 (c) 47 (d) 319
  39. 39.Which term of the AP 7, 16, 25, 34, … is 106? (a) 11th (b) 12th (c) 14th (d) 13th
  40. 40.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 31 (b) 240 (c) 480 (d) 252

Answer key

  1. 55
  2. 99
  3. 38th
  4. 39
  5. 54
  6. 9
  7. 349
  8. 103
  9. 26th
  10. 176
  11. 29th
  12. 29th
  13. 165
  14. 153
  15. 120
  16. 196
  17. 18
  18. 65
  19. 121
  20. 40
  21. 27
  22. 1326
  23. 117
  24. 12th
  25. 136
  26. 64
  27. 529
  28. 82
  29. 256
  30. 66
  31. 253
  32. 676
  33. 90
  34. 124
  35. 324
  36. 20
  37. 21st
  38. 297
  39. 12th
  40. 240

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