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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 449 · 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 3, 7, 11, …? (a) 47 (b) 300 (c) 600 (d) 324
  2. 2.What is the 25th term of the AP 19, 21, 23, 25, …? (a) 48 (b) 69 (c) 67 (d) 50
  3. 3.Which term of the AP 10, 15, 20, 25, … is 65? (a) 11th (b) 14th (c) 13th (d) 12th
  4. 4.Which term of the AP 7, 10, 13, 16, … is 55? (a) 18th (b) 16th (c) 19th (d) 17th
  5. 5.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 18 (b) 88 (c) 176 (d) 96
  6. 6.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  7. 7.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2450 (d) 2485
  8. 8.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 5112 (c) 2557 (d) 2556
  9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 870 (d) 57
  10. 10.Which term of the AP 7, 16, 25, 34, … is 142? (a) 15th (b) 16th (c) 17th (d) 18th
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  12. 12.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 240 (b) 444 (c) 222 (d) 35
  13. 13.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 242 (c) 253 (d) 231
  14. 14.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 112 (b) 216 (c) 108 (d) 17
  15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  17. 17.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 210 (d) 231
  18. 18.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 276 (d) 277
  19. 19.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 174 (b) 348 (c) 180 (d) 20
  20. 20.What is the 16th term of the AP 7, 14, 21, 28, …? (a) 119 (b) 112 (c) 113 (d) 105
  21. 21.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 203 (b) 364 (c) 44 (d) 182
  22. 22.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 28 (b) 152 (c) 280 (d) 140
  23. 23.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 31 (b) 32 (c) 30 (d) 38
  24. 24.Which term of the AP 3, 11, 19, 27, … is 139? (a) 20th (b) 18th (c) 17th (d) 19th
  25. 25.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 72 (b) 144 (c) 17 (d) 78
  26. 26.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 119 (b) 27 (c) 210 (d) 105
  27. 27.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 162 (b) 324 (c) 165 (d) 30
  28. 28.What is the 13th term of the AP 5, 10, 15, 20, …? (a) 70 (b) 60 (c) 66 (d) 65
  29. 29.What is the 30th term of the AP 14, 18, 22, 26, …? (a) 120 (b) 130 (c) 116 (d) 134
  30. 30.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  31. 31.What is the 18th term of the AP 10, 12, 14, 16, …? (a) 34 (b) 36 (c) 46 (d) 44
  32. 32.What is the 40th term of the AP 4, 11, 18, 25, …? (a) 284 (b) 280 (c) 277 (d) 273
  33. 33.What is the 33rd term of the AP 17, 20, 23, 26, …? (a) 116 (b) 99 (c) 113 (d) 96
  34. 34.Which term of the AP 10, 19, 28, 37, … is 235? (a) 26th (b) 27th (c) 28th (d) 25th
  35. 35.What is the 29th term of the AP 17, 25, 33, 41, …? (a) 249 (b) 241 (c) 232 (d) 224
  36. 36.What is the 37th term of the AP 7, 12, 17, 22, …? (a) 180 (b) 192 (c) 185 (d) 187
  37. 37.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 23 (b) 28 (c) 24 (d) 25
  38. 38.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 99 (b) 198 (c) 114 (d) 29
  39. 39.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 4160 (c) 2016 (d) 2080
  40. 40.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 26 (b) 29 (c) 25 (d) 24

Answer key

  1. 300
  2. 67
  3. 12th
  4. 17th
  5. 88
  6. 100
  7. 2485
  8. 2556
  9. 841
  10. 16th
  11. 144
  12. 222
  13. 253
  14. 108
  15. 36
  16. 81
  17. 231
  18. 276
  19. 174
  20. 112
  21. 182
  22. 140
  23. 31
  24. 18th
  25. 72
  26. 105
  27. 162
  28. 65
  29. 130
  30. 676
  31. 44
  32. 277
  33. 113
  34. 26th
  35. 241
  36. 187
  37. 24
  38. 99
  39. 2080
  40. 25

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