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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 70 · 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 4, ?, 12, 16, 20? (a) 12 (b) 7 (c) 8 (d) 9
  2. 2.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 190 (b) 110 (c) 31 (d) 95
  3. 3.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3486 (c) 6972 (d) 3403
  4. 4.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 8 (b) 10 (c) 12 (d) 9
  5. 5.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 140 (b) 130 (c) 260 (d) 22
  6. 6.What is the 21st term of the AP 3, 8, 13, 18, …? (a) 103 (b) 105 (c) 108 (d) 100
  7. 7.What is the 25th term of the AP 18, 25, 32, 39, …? (a) 175 (b) 186 (c) 193 (d) 168
  8. 8.Which term of the AP 17, 21, 25, 29, … is 89? (a) 19th (b) 21st (c) 20th (d) 18th
  9. 9.What is the 40th term of the AP 8, 14, 20, 26, …? (a) 248 (b) 234 (c) 240 (d) 242
  10. 10.Which term of the AP 10, 15, 20, 25, … is 135? (a) 27th (b) 28th (c) 25th (d) 26th
  11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
  12. 12.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 342 (c) 162 (d) 171
  13. 13.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 78 (d) 156
  14. 14.What is the 18th term of the AP 3, 9, 15, 21, …? (a) 105 (b) 108 (c) 111 (d) 102
  15. 15.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 49 (b) 252 (c) 225 (d) 450
  16. 16.Which term of the AP 2, 5, 8, 11, … is 86? (a) 31st (b) 30th (c) 28th (d) 29th
  17. 17.What is the 26th term of the AP 1, 9, 17, 25, …? (a) 208 (b) 209 (c) 201 (d) 200
  18. 18.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 7 (b) 9 (c) 5 (d) 6
  19. 19.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 612 (c) 42 (d) 324
  20. 20.Which term of the AP 17, 25, 33, 41, … is 289? (a) 34th (b) 35th (c) 37th (d) 36th
  21. 21.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 64 (c) 60 (d) 120
  22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  23. 23.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 25 (d) 91
  24. 24.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4278 (c) 4371 (d) 4372
  25. 25.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
  26. 26.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 20 (b) 21 (c) 24 (d) 22
  27. 27.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 277 (c) 552 (d) 253
  28. 28.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 234 (b) 231 (c) 462 (d) 36
  29. 29.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 182 (c) 41 (d) 161
  30. 30.What is the 26th term of the AP 6, 13, 20, 27, …? (a) 181 (b) 182 (c) 175 (d) 188
  31. 31.What is the 23rd term of the AP 6, 9, 12, 15, …? (a) 69 (b) 75 (c) 72 (d) 66
  32. 32.What is the 31st term of the AP 8, 12, 16, 20, …? (a) 128 (b) 120 (c) 124 (d) 132
  33. 33.What is the 36th term of the AP 6, 8, 10, 12, …? (a) 72 (b) 70 (c) 76 (d) 78
  34. 34.What is the 25th term of the AP 6, 8, 10, 12, …? (a) 56 (b) 54 (c) 50 (d) 48
  35. 35.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 46 (b) 90 (c) 45 (d) 9
  36. 36.Which term of the AP 15, 17, 19, 21, … is 73? (a) 30th (b) 29th (c) 32nd (d) 31st
  37. 37.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 564 (b) 40 (c) 282 (d) 300
  38. 38.What is the 15th term of the AP 8, 14, 20, 26, …? (a) 98 (b) 92 (c) 84 (d) 90
  39. 39.What is the 27th term of the AP 14, 19, 24, 29, …? (a) 135 (b) 144 (c) 149 (d) 130
  40. 40.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 70 (b) 19 (c) 73 (d) 140

Answer key

  1. 8
  2. 95
  3. 3486
  4. 9
  5. 130
  6. 103
  7. 186
  8. 19th
  9. 242
  10. 26th
  11. 25
  12. 171
  13. 78
  14. 105
  15. 225
  16. 29th
  17. 201
  18. 6
  19. 306
  20. 35th
  21. 60
  22. 841
  23. 169
  24. 4371
  25. 196
  26. 21
  27. 276
  28. 231
  29. 161
  30. 181
  31. 72
  32. 128
  33. 76
  34. 54
  35. 45
  36. 30th
  37. 282
  38. 92
  39. 144
  40. 70

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