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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 702 · 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 12th term of the AP 2, 4, 6, 8, …? (a) 24 (b) 26 (c) 25 (d) 22
  2. 2.What is the 38th term of the AP 7, 9, 11, 13, …? (a) 76 (b) 81 (c) 83 (d) 74
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 105 (d) 27
  4. 4.Which term of the AP 9, 12, 15, 18, … is 111? (a) 36th (b) 35th (c) 37th (d) 34th
  5. 5.What is the 39th term of the AP 8, 17, 26, 35, …? (a) 342 (b) 351 (c) 359 (d) 350
  6. 6.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 220 (b) 15 (c) 111 (d) 110
  7. 7.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 39 (b) 30 (c) 29 (d) 31
  8. 8.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 2450 (c) 2485 (d) 4970
  9. 9.Which term of the AP 13, 20, 27, 34, … is 153? (a) 23rd (b) 20th (c) 21st (d) 22nd
  10. 10.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1081 (c) 1128 (d) 1129
  11. 11.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 15 (c) 84 (d) 168
  12. 12.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 2851 (c) 5700 (d) 2775
  13. 13.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 248 (b) 272 (c) 52 (d) 496
  14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  15. 15.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 351 (d) 702
  16. 16.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 75 (c) 140 (d) 70
  17. 17.What is the 28th term of the AP 4, 7, 10, 13, …? (a) 85 (b) 81 (c) 84 (d) 88
  18. 18.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
  20. 20.Which term of the AP 19, 26, 33, 40, … is 124? (a) 18th (b) 16th (c) 15th (d) 17th
  21. 21.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 29 (b) 28 (c) 35 (d) 30
  22. 22.Which term of the AP 9, 13, 17, 21, … is 129? (a) 32nd (b) 30th (c) 33rd (d) 31st
  23. 23.Which term of the AP 14, 17, 20, 23, … is 80? (a) 22nd (b) 24th (c) 23rd (d) 25th
  24. 24.Which term of the AP 18, 24, 30, 36, … is 114? (a) 19th (b) 16th (c) 17th (d) 18th
  25. 25.What is the 13th term of the AP 7, 14, 21, 28, …? (a) 84 (b) 98 (c) 92 (d) 91
  26. 26.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 290 (b) 540 (c) 270 (d) 45
  27. 27.What is the 25th term of the AP 4, 10, 16, 22, …? (a) 154 (b) 150 (c) 148 (d) 144
  28. 28.What is the 25th term of the AP 1, 4, 7, 10, …? (a) 72 (b) 73 (c) 76 (d) 75
  29. 29.Which term of the AP 16, 18, 20, 22, … is 48? (a) 17th (b) 16th (c) 18th (d) 24th
  30. 30.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 741 (c) 703 (d) 1482
  31. 31.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 11 (b) 12 (c) 17 (d) 13
  32. 32.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 55 (c) 110 (d) 10
  33. 33.What is the 17th term of the AP 14, 16, 18, 20, …? (a) 34 (b) 32 (c) 48 (d) 46
  34. 34.What is the 22nd term of the AP 20, 29, 38, 47, …? (a) 209 (b) 189 (c) 198 (d) 218
  35. 35.What is the 23rd term of the AP 19, 26, 33, 40, …? (a) 154 (b) 180 (c) 161 (d) 173
  36. 36.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 11 (b) 54 (c) 102 (d) 51
  37. 37.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 286 (b) 572 (c) 46 (d) 308
  38. 38.Which term of the AP 4, 8, 12, 16, … is 148? (a) 39th (b) 38th (c) 37th (d) 36th
  39. 39.What is the 17th term of the AP 20, 27, 34, 41, …? (a) 112 (b) 139 (c) 119 (d) 132
  40. 40.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 27 (b) 22 (c) 24 (d) 23

Answer key

  1. 24
  2. 81
  3. 196
  4. 35th
  5. 350
  6. 110
  7. 30
  8. 2485
  9. 21st
  10. 1128
  11. 84
  12. 2850
  13. 248
  14. 729
  15. 676
  16. 70
  17. 85
  18. 49
  19. 361
  20. 16th
  21. 29
  22. 31st
  23. 23rd
  24. 17th
  25. 91
  26. 270
  27. 148
  28. 73
  29. 17th
  30. 741
  31. 12
  32. 55
  33. 46
  34. 209
  35. 173
  36. 51
  37. 286
  38. 37th
  39. 132
  40. 23

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