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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 497 · 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 2, ?, 12, 17, 22? (a) 12 (b) 7 (c) 8 (d) 6
  2. 2.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 7656 (c) 3741 (d) 3828
  3. 3.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 120 (b) 230 (c) 16 (d) 115
  4. 4.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 150 (b) 168 (c) 300 (d) 40
  5. 5.What is the 14th term of the AP 2, 7, 12, 17, …? (a) 65 (b) 67 (c) 72 (d) 70
  6. 6.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1654 (c) 1653 (d) 3306
  7. 7.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 49 (b) 348 (c) 648 (d) 324
  8. 8.What is the 25th term of the AP 16, 23, 30, 37, …? (a) 168 (b) 191 (c) 184 (d) 175
  9. 9.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 384 (c) 354 (d) 57
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 272 (d) 31
  11. 11.What is the 23rd term of the AP 3, 6, 9, 12, …? (a) 66 (b) 69 (c) 70 (d) 72
  12. 12.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 50 (c) 55 (d) 100
  13. 13.What is the 15th term of the AP 14, 23, 32, 41, …? (a) 126 (b) 135 (c) 140 (d) 149
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 15 (d) 36
  15. 15.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 110 (b) 19 (c) 55 (d) 65
  16. 16.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 17 (b) 144 (c) 138 (d) 276
  17. 17.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3486 (c) 3403 (d) 6972
  18. 18.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 24 (c) 99 (d) 108
  19. 19.Which term of the AP 3, 12, 21, 30, … is 138? (a) 18th (b) 15th (c) 16th (d) 17th
  20. 20.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 400 (b) 220 (c) 38 (d) 200
  21. 21.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 126 (b) 30 (c) 140 (d) 252
  22. 22.Which term of the AP 19, 23, 27, 31, … is 67? (a) 12th (b) 14th (c) 15th (d) 13th
  23. 23.What is the 28th term of the AP 12, 21, 30, 39, …? (a) 243 (b) 255 (c) 264 (d) 252
  24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 325 (d) 49
  25. 25.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 133 (c) 147 (d) 31
  26. 26.What is the missing term in the AP 13, 16, 19, ?, 25? (a) 23 (b) 25 (c) 21 (d) 22
  27. 27.What is the 15th term of the AP 4, 8, 12, 16, …? (a) 64 (b) 61 (c) 56 (d) 60
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 36 (d) 21
  29. 29.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 702 (c) 325 (d) 338
  30. 30.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 22 (b) 24 (c) 29 (d) 23
  31. 31.Which term of the AP 13, 20, 27, 34, … is 195? (a) 29th (b) 26th (c) 27th (d) 28th
  32. 32.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 9900 (c) 4950 (d) 4851
  33. 33.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 20 (b) 19 (c) 18 (d) 25
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  35. 35.What is the 31st term of the AP 16, 23, 30, 37, …? (a) 210 (b) 233 (c) 217 (d) 226
  36. 36.What is the 39th term of the AP 6, 10, 14, 18, …? (a) 162 (b) 152 (c) 156 (d) 158
  37. 37.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 418 (b) 220 (c) 209 (d) 29
  38. 38.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
  39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 225 (d) 29
  40. 40.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 1406 (c) 703 (d) 666

Answer key

  1. 7
  2. 3828
  3. 115
  4. 150
  5. 67
  6. 1653
  7. 324
  8. 184
  9. 354
  10. 256
  11. 69
  12. 50
  13. 140
  14. 64
  15. 55
  16. 138
  17. 3486
  18. 99
  19. 16th
  20. 200
  21. 126
  22. 13th
  23. 255
  24. 625
  25. 133
  26. 22
  27. 60
  28. 36
  29. 351
  30. 23
  31. 27th
  32. 4950
  33. 19
  34. 25
  35. 226
  36. 158
  37. 209
  38. 729
  39. 225
  40. 703

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