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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 77 · 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.Which term of the AP 13, 17, 21, 25, … is 93? (a) 22nd (b) 20th (c) 23rd (d) 21st
  2. 2.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 372 (c) 56 (d) 342
  3. 3.What is the 37th term of the AP 1, 4, 7, 10, …? (a) 112 (b) 111 (c) 108 (d) 109
  4. 4.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 12 (b) 11 (c) 10 (d) 14
  5. 5.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 540 (b) 50 (c) 275 (d) 270
  6. 6.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 11 (c) 35 (d) 40
  7. 7.Which term of the AP 16, 23, 30, 37, … is 233? (a) 34th (b) 32nd (c) 31st (d) 33rd
  8. 8.What is the 15th term of the AP 4, 12, 20, 28, …? (a) 124 (b) 112 (c) 116 (d) 120
  9. 9.What is the 14th term of the AP 19, 24, 29, 34, …? (a) 70 (b) 65 (c) 84 (d) 89
  10. 10.What is the 36th term of the AP 8, 10, 12, 14, …? (a) 70 (b) 72 (c) 80 (d) 78
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
  12. 12.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 66 (c) 72 (d) 156
  13. 13.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 81 (b) 78 (c) 92 (d) 89
  14. 14.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 24 (b) 25 (c) 29 (d) 23
  15. 15.Which term of the AP 17, 19, 21, 23, … is 35? (a) 10th (b) 11th (c) 12th (d) 9th
  16. 16.Which term of the AP 5, 7, 9, 11, … is 71? (a) 35th (b) 36th (c) 33rd (d) 34th
  17. 17.What is the 39th term of the AP 9, 11, 13, 15, …? (a) 76 (b) 87 (c) 85 (d) 78
  18. 18.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 7832 (d) 3916
  19. 19.Which term of the AP 16, 22, 28, 34, … is 106? (a) 17th (b) 16th (c) 15th (d) 18th
  20. 20.What is the 30th term of the AP 2, 8, 14, 20, …? (a) 176 (b) 174 (c) 182 (d) 180
  21. 21.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  22. 22.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 154 (b) 133 (c) 266 (d) 37
  23. 23.What is the 19th term of the AP 4, 8, 12, 16, …? (a) 72 (b) 80 (c) 76 (d) 77
  24. 24.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 648 (b) 324 (c) 348 (d) 49
  25. 25.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 253 (d) 43
  26. 26.Which term of the AP 10, 16, 22, 28, … is 82? (a) 12th (b) 14th (c) 15th (d) 13th
  27. 27.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  28. 28.What is the 39th term of the AP 3, 6, 9, 12, …? (a) 118 (b) 114 (c) 117 (d) 120
  29. 29.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 54 (b) 108 (c) 10 (d) 55
  30. 30.Which term of the AP 1, 6, 11, 16, … is 46? (a) 12th (b) 11th (c) 9th (d) 10th
  31. 31.What is the 28th term of the AP 17, 20, 23, 26, …? (a) 101 (b) 98 (c) 81 (d) 84
  32. 32.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2145 (d) 2211
  33. 33.What is the 10th term of the AP 4, 12, 20, 28, …? (a) 72 (b) 76 (c) 80 (d) 84
  34. 34.What is the 30th term of the AP 6, 15, 24, 33, …? (a) 270 (b) 261 (c) 267 (d) 276
  35. 35.Which term of the AP 11, 14, 17, 20, … is 119? (a) 39th (b) 36th (c) 38th (d) 37th
  36. 36.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 156 (b) 12 (c) 84 (d) 78
  37. 37.What is the 30th term of the AP 14, 20, 26, 32, …? (a) 194 (b) 188 (c) 180 (d) 174
  38. 38.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 25 (b) 120 (c) 234 (d) 117
  39. 39.What is the missing term in the AP 19, 25, ?, 37, 43? (a) 30 (b) 37 (c) 31 (d) 32
  40. 40.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 18 (b) 22 (c) 17 (d) 19

Answer key

  1. 21st
  2. 342
  3. 109
  4. 11
  5. 270
  6. 35
  7. 32nd
  8. 116
  9. 84
  10. 78
  11. 576
  12. 78
  13. 89
  14. 24
  15. 10th
  16. 34th
  17. 85
  18. 3916
  19. 16th
  20. 176
  21. 100
  22. 133
  23. 76
  24. 324
  25. 484
  26. 13th
  27. 64
  28. 117
  29. 54
  30. 10th
  31. 98
  32. 2211
  33. 76
  34. 267
  35. 37th
  36. 78
  37. 188
  38. 117
  39. 31
  40. 18

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