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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 343 · 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 all the whole numbers from 1 to 31? (a) 496 (b) 497 (c) 992 (d) 465
  2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
  3. 3.What is the 17th term of the AP 1, 8, 15, 22, …? (a) 119 (b) 112 (c) 113 (d) 120
  4. 4.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 59 (b) 378 (c) 408 (d) 756
  5. 5.Which term of the AP 9, 14, 19, 24, … is 189? (a) 38th (b) 36th (c) 39th (d) 37th
  6. 6.Which term of the AP 16, 18, 20, 22, … is 88? (a) 36th (b) 44th (c) 38th (d) 37th
  7. 7.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 9 (b) 7 (c) 15 (d) 8
  8. 8.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 540 (b) 288 (c) 270 (d) 39
  9. 9.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 65 (b) 60 (c) 120 (d) 22
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 351 (d) 676
  11. 11.What is the 26th term of the AP 7, 9, 11, 13, …? (a) 59 (b) 50 (c) 52 (d) 57
  12. 12.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1275 (c) 1327 (d) 1326
  13. 13.What is the 16th term of the AP 4, 12, 20, 28, …? (a) 124 (b) 128 (c) 120 (d) 132
  14. 14.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 21 (b) 19 (c) 18 (d) 20
  15. 15.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 176 (c) 26 (d) 352
  16. 16.What is the 10th term of the AP 12, 16, 20, 24, …? (a) 52 (b) 48 (c) 40 (d) 36
  17. 17.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 800 (c) 780 (d) 1640
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 120 (d) 240
  19. 19.What is the missing term in the AP 9, 18, ?, 36, 45? (a) 26 (b) 27 (c) 28 (d) 36
  20. 20.Which term of the AP 9, 12, 15, 18, … is 54? (a) 17th (b) 18th (c) 15th (d) 16th
  21. 21.Which term of the AP 10, 19, 28, 37, … is 73? (a) 10th (b) 9th (c) 8th (d) 7th
  22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
  23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  24. 24.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 336 (b) 189 (c) 42 (d) 168
  25. 25.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 15 (d) 64
  26. 26.What is the 40th term of the AP 10, 14, 18, 22, …? (a) 170 (b) 160 (c) 156 (d) 166
  27. 27.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 36 (b) 72 (c) 40 (d) 8
  28. 28.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 45 (b) 37 (c) 36 (d) 35
  29. 29.Which term of the AP 4, 6, 8, 10, … is 60? (a) 28th (b) 30th (c) 29th (d) 31st
  30. 30.What is the 18th term of the AP 20, 26, 32, 38, …? (a) 102 (b) 122 (c) 128 (d) 108
  31. 31.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1176 (c) 1226 (d) 1225
  32. 32.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1891 (c) 1953 (d) 3906
  33. 33.What is the 32nd term of the AP 15, 21, 27, 33, …? (a) 186 (b) 207 (c) 201 (d) 192
  34. 34.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 216 (c) 432 (d) 29
  35. 35.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 812 (d) 406
  36. 36.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 171 (c) 153 (d) 342
  37. 37.What is the 21st term of the AP 8, 11, 14, 17, …? (a) 71 (b) 60 (c) 68 (d) 63
  38. 38.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 558 (b) 279 (c) 55 (d) 306
  39. 39.What is the 40th term of the AP 3, 10, 17, 24, …? (a) 280 (b) 283 (c) 276 (d) 273
  40. 40.What is the 11th term of the AP 12, 20, 28, 36, …? (a) 88 (b) 100 (c) 80 (d) 92

Answer key

  1. 496
  2. 196
  3. 113
  4. 378
  5. 37th
  6. 37th
  7. 8
  8. 270
  9. 60
  10. 676
  11. 57
  12. 1326
  13. 124
  14. 19
  15. 176
  16. 48
  17. 820
  18. 225
  19. 27
  20. 16th
  21. 8th
  22. 576
  23. 729
  24. 168
  25. 64
  26. 166
  27. 36
  28. 36
  29. 29th
  30. 122
  31. 1225
  32. 1953
  33. 201
  34. 216
  35. 784
  36. 171
  37. 68
  38. 279
  39. 276
  40. 92

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