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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 144 · 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 9 terms of the AP 6, 8, 10, …? (a) 22 (b) 126 (c) 135 (d) 252
  2. 2.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 253 (c) 484 (d) 43
  3. 3.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1682 (c) 3422 (d) 1711
  4. 4.What is the 22nd term of the AP 10, 13, 16, 19, …? (a) 73 (b) 63 (c) 66 (d) 76
  5. 5.What is the 13th term of the AP 13, 16, 19, 22, …? (a) 36 (b) 39 (c) 49 (d) 52
  6. 6.What is the 33rd term of the AP 11, 15, 19, 23, …? (a) 143 (b) 128 (c) 132 (d) 139
  7. 7.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 41 (b) 32 (c) 33 (d) 31
  8. 8.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 266 (b) 138 (c) 133 (d) 34
  9. 9.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 9 (b) 6 (c) 7 (d) 8
  10. 10.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 28 (b) 23 (c) 24 (d) 25
  11. 11.What is the 34th term of the AP 1, 10, 19, 28, …? (a) 307 (b) 297 (c) 306 (d) 298
  12. 12.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2485 (d) 2450
  13. 13.What is the 21st term of the AP 7, 11, 15, 19, …? (a) 80 (b) 84 (c) 91 (d) 87
  14. 14.What is the 16th term of the AP 12, 14, 16, 18, …? (a) 32 (b) 44 (c) 42 (d) 30
  15. 15.Which term of the AP 5, 9, 13, 17, … is 97? (a) 24th (b) 25th (c) 23rd (d) 26th
  16. 16.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 85 (c) 26 (d) 80
  17. 17.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 255 (b) 280 (c) 510 (d) 48
  18. 18.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 286 (b) 18 (c) 144 (d) 143
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 72 (d) 15
  20. 20.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
  21. 21.What is the 15th term of the AP 10, 16, 22, 28, …? (a) 94 (b) 90 (c) 84 (d) 100
  22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 729 (d) 53
  23. 23.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 23 (b) 22 (c) 24 (d) 29
  24. 24.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 55 (b) 110 (c) 17 (d) 58
  25. 25.What is the 11th term of the AP 11, 13, 15, 17, …? (a) 33 (b) 20 (c) 22 (d) 31
  26. 26.What is the 21st term of the AP 7, 10, 13, 16, …? (a) 70 (b) 60 (c) 67 (d) 63
  27. 27.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 54 (c) 14 (d) 108
  28. 28.Which term of the AP 4, 9, 14, 19, … is 184? (a) 36th (b) 39th (c) 37th (d) 38th
  29. 29.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 286 (b) 528 (c) 44 (d) 264
  30. 30.What is the 19th term of the AP 20, 23, 26, 29, …? (a) 77 (b) 57 (c) 54 (d) 74
  31. 31.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3570 (c) 7140 (d) 3528
  32. 32.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 25 (b) 29 (c) 23 (d) 24
  33. 33.What is the 39th term of the AP 11, 14, 17, 20, …? (a) 114 (b) 125 (c) 128 (d) 117
  34. 34.Which term of the AP 19, 24, 29, 34, … is 194? (a) 37th (b) 35th (c) 36th (d) 38th
  35. 35.What is the 14th term of the AP 11, 15, 19, 23, …? (a) 67 (b) 52 (c) 56 (d) 63
  36. 36.What is the 11th term of the AP 11, 20, 29, 38, …? (a) 110 (b) 99 (c) 101 (d) 90
  37. 37.Which term of the AP 12, 15, 18, 21, … is 51? (a) 13th (b) 17th (c) 14th (d) 15th
  38. 38.What is the 13th term of the AP 20, 22, 24, 26, …? (a) 24 (b) 44 (c) 26 (d) 46
  39. 39.What is the missing term in the AP 19, 25, ?, 37, 43? (a) 32 (b) 37 (c) 30 (d) 31
  40. 40.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 126 (b) 252 (c) 18 (d) 127

Answer key

  1. 126
  2. 484
  3. 1711
  4. 73
  5. 49
  6. 139
  7. 32
  8. 133
  9. 7
  10. 24
  11. 298
  12. 2485
  13. 87
  14. 42
  15. 24th
  16. 80
  17. 255
  18. 143
  19. 64
  20. 361
  21. 94
  22. 729
  23. 23
  24. 55
  25. 31
  26. 67
  27. 54
  28. 37th
  29. 264
  30. 74
  31. 3570
  32. 24
  33. 125
  34. 36th
  35. 63
  36. 101
  37. 14th
  38. 44
  39. 31
  40. 126

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