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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 51 · 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 18, ?, 34, 42, 50? (a) 27 (b) 26 (c) 34 (d) 25
  2. 2.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 17 (b) 18 (c) 20 (d) 16
  3. 3.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 45 (c) 13 (d) 50
  4. 4.Which term of the AP 11, 15, 19, 23, … is 47? (a) 10th (b) 9th (c) 11th (d) 12th
  5. 5.What is the 16th term of the AP 12, 17, 22, 27, …? (a) 92 (b) 80 (c) 87 (d) 75
  6. 6.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 270 (c) 490 (d) 245
  7. 7.What is the 38th term of the AP 20, 27, 34, 41, …? (a) 259 (b) 286 (c) 266 (d) 279
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 81 (d) 45
  9. 9.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 216 (b) 198 (c) 396 (d) 38
  10. 10.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  11. 11.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1250 (c) 1225 (d) 2550
  12. 12.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 72 (b) 126 (c) 63 (d) 18
  13. 13.What is the 39th term of the AP 4, 8, 12, 16, …? (a) 156 (b) 160 (c) 152 (d) 157
  14. 14.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 252 (b) 279 (c) 52 (d) 504
  15. 15.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 21 (c) 121 (d) 132
  16. 16.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 32 (b) 30 (c) 31 (d) 39
  17. 17.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 2556 (c) 5256 (d) 2628
  18. 18.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 13 (d) 49
  19. 19.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  20. 20.Which term of the AP 3, 6, 9, 12, … is 24? (a) 10th (b) 8th (c) 9th (d) 7th
  21. 21.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 38 (b) 33 (c) 32 (d) 31
  22. 22.What is the 21st term of the AP 11, 14, 17, 20, …? (a) 74 (b) 71 (c) 60 (d) 63
  23. 23.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 130 (b) 17 (c) 250 (d) 125
  24. 24.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 18 (c) 60 (d) 120
  25. 25.What is the 35th term of the AP 4, 8, 12, 16, …? (a) 141 (b) 144 (c) 140 (d) 136
  26. 26.What is the 12th term of the AP 10, 12, 14, 16, …? (a) 34 (b) 22 (c) 24 (d) 32
  27. 27.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 351 (c) 378 (d) 756
  28. 28.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1711 (c) 3540 (d) 1770
  29. 29.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 12 (b) 84 (c) 156 (d) 78
  30. 30.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 9900 (c) 4951 (d) 4851
  31. 31.What is the missing term in the AP 4, 12, 20, ?, 36? (a) 29 (b) 27 (c) 36 (d) 28
  32. 32.What is the 23rd term of the AP 1, 6, 11, 16, …? (a) 115 (b) 111 (c) 116 (d) 110
  33. 33.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 33 (b) 126 (c) 108 (d) 216
  34. 34.What is the 17th term of the AP 14, 22, 30, 38, …? (a) 136 (b) 128 (c) 142 (d) 150
  35. 35.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 43 (c) 270 (d) 250
  36. 36.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 37 (b) 308 (c) 154 (d) 159
  37. 37.What is the 20th term of the AP 16, 21, 26, 31, …? (a) 100 (b) 111 (c) 116 (d) 95
  38. 38.What is the missing term in the AP 20, 29, 38, ?, 56? (a) 48 (b) 46 (c) 47 (d) 56
  39. 39.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 306 (b) 156 (c) 29 (d) 153
  40. 40.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 13 (b) 170 (c) 90 (d) 85

Answer key

  1. 26
  2. 17
  3. 45
  4. 10th
  5. 87
  6. 245
  7. 279
  8. 81
  9. 198
  10. 225
  11. 1275
  12. 63
  13. 156
  14. 252
  15. 121
  16. 31
  17. 2628
  18. 49
  19. 406
  20. 8th
  21. 32
  22. 71
  23. 125
  24. 60
  25. 140
  26. 32
  27. 378
  28. 1770
  29. 78
  30. 4950
  31. 28
  32. 111
  33. 108
  34. 142
  35. 250
  36. 154
  37. 111
  38. 47
  39. 153
  40. 85

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