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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 444 · 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 92? (a) 4232 (b) 4186 (c) 8556 (d) 4278
  2. 2.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3321 (c) 6806 (d) 3362
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 441 (d) 462
  4. 4.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 4 (b) 3 (c) 6 (d) 5
  5. 5.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 49 (b) 319 (c) 341 (d) 638
  6. 6.What is the missing term in the AP 13, 16, 19, ?, 25? (a) 21 (b) 25 (c) 22 (d) 23
  7. 7.What is the 35th term of the AP 7, 15, 23, 31, …? (a) 279 (b) 280 (c) 287 (d) 272
  8. 8.Which term of the AP 10, 16, 22, 28, … is 214? (a) 37th (b) 34th (c) 35th (d) 36th
  9. 9.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 616 (b) 313 (c) 308 (d) 53
  10. 10.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 21 (b) 19 (c) 26 (d) 20
  11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
  12. 12.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 1332 (c) 648 (d) 666
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  14. 14.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 440 (b) 880 (c) 473 (d) 70
  15. 15.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 9 (b) 8 (c) 7 (d) 14
  16. 16.What is the 29th term of the AP 20, 24, 28, 32, …? (a) 112 (b) 136 (c) 116 (d) 132
  17. 17.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  18. 18.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 580 (b) 320 (c) 290 (d) 56
  19. 19.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 6 (b) 8 (c) 9 (d) 7
  20. 20.What is the 11th term of the AP 6, 13, 20, 27, …? (a) 76 (b) 77 (c) 70 (d) 83
  21. 21.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 5256 (c) 2628 (d) 2556
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  23. 23.What is the 29th term of the AP 15, 23, 31, 39, …? (a) 232 (b) 224 (c) 239 (d) 247
  24. 24.What is the 29th term of the AP 2, 9, 16, 23, …? (a) 205 (b) 196 (c) 198 (d) 203
  25. 25.What is the 32nd term of the AP 2, 5, 8, 11, …? (a) 93 (b) 98 (c) 96 (d) 95
  26. 26.What is the 14th term of the AP 6, 13, 20, 27, …? (a) 104 (b) 91 (c) 98 (d) 97
  27. 27.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 57 (c) 114 (d) 12
  28. 28.Which term of the AP 5, 13, 21, 29, … is 93? (a) 11th (b) 14th (c) 13th (d) 12th
  29. 29.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 168 (b) 85 (c) 84 (d) 15
  30. 30.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 24 (b) 21 (c) 22 (d) 23
  31. 31.What is the 16th term of the AP 7, 10, 13, 16, …? (a) 48 (b) 52 (c) 45 (d) 55
  32. 32.What is the 25th term of the AP 1, 9, 17, 25, …? (a) 200 (b) 201 (c) 192 (d) 193
  33. 33.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 29 (b) 30 (c) 28 (d) 33
  34. 34.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
  36. 36.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 78 (c) 66 (d) 72
  37. 37.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 144 (b) 30 (c) 128 (d) 256
  38. 38.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 23 (b) 24 (c) 33 (d) 25
  39. 39.What is the 11th term of the AP 8, 12, 16, 20, …? (a) 40 (b) 48 (c) 44 (d) 52
  40. 40.What is the 12th term of the AP 2, 6, 10, 14, …? (a) 44 (b) 46 (c) 48 (d) 50

Answer key

  1. 4278
  2. 3403
  3. 441
  4. 4
  5. 319
  6. 22
  7. 279
  8. 35th
  9. 308
  10. 20
  11. 196
  12. 666
  13. 49
  14. 440
  15. 8
  16. 132
  17. 256
  18. 290
  19. 7
  20. 76
  21. 2628
  22. 121
  23. 239
  24. 198
  25. 95
  26. 97
  27. 57
  28. 12th
  29. 84
  30. 22
  31. 52
  32. 193
  33. 29
  34. 64
  35. 529
  36. 78
  37. 128
  38. 24
  39. 48
  40. 46

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