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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 312 · 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 32nd term of the AP 1, 9, 17, 25, …? (a) 249 (b) 256 (c) 248 (d) 257
  2. 2.What is the 25th term of the AP 5, 7, 9, 11, …? (a) 55 (b) 50 (c) 53 (d) 48
  3. 3.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 756 (d) 378
  4. 4.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 41 (b) 50 (c) 42 (d) 43
  5. 5.What is the 10th term of the AP 10, 15, 20, 25, …? (a) 45 (b) 55 (c) 60 (d) 50
  6. 6.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 26 (b) 22 (c) 21 (d) 20
  7. 7.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 19 (b) 21 (c) 20 (d) 23
  8. 8.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 288 (c) 300 (d) 600
  9. 9.What is the 36th term of the AP 11, 13, 15, 17, …? (a) 81 (b) 83 (c) 70 (d) 72
  10. 10.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 25 (b) 29 (c) 23 (d) 24
  11. 11.Which term of the AP 7, 15, 23, 31, … is 303? (a) 40th (b) 38th (c) 39th (d) 37th
  12. 12.What is the 32nd term of the AP 5, 9, 13, 17, …? (a) 133 (b) 124 (c) 129 (d) 128
  13. 13.What is the 13th term of the AP 1, 6, 11, 16, …? (a) 60 (b) 66 (c) 61 (d) 65
  14. 14.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 14 (b) 20 (c) 16 (d) 15
  15. 15.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 4005 (c) 3916 (d) 8010
  16. 16.What is the 27th term of the AP 1, 8, 15, 22, …? (a) 189 (b) 183 (c) 190 (d) 182
  17. 17.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 40 (b) 550 (c) 275 (d) 278
  18. 18.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 198 (b) 99 (c) 14 (d) 100
  19. 19.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 190 (c) 27 (d) 180
  20. 20.What is the 32nd term of the AP 11, 13, 15, 17, …? (a) 75 (b) 62 (c) 73 (d) 64
  21. 21.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  22. 22.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 53 (b) 45 (c) 44 (d) 43
  23. 23.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 5 (b) 6 (c) 7 (d) 10
  24. 24.What is the 27th term of the AP 13, 20, 27, 34, …? (a) 195 (b) 202 (c) 189 (d) 182
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 625 (d) 325
  26. 26.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 105 (d) 210
  27. 27.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 288 (b) 28 (c) 147 (d) 144
  28. 28.What is the 22nd term of the AP 13, 16, 19, 22, …? (a) 76 (b) 79 (c) 66 (d) 63
  29. 29.What is the 39th term of the AP 9, 12, 15, 18, …? (a) 126 (b) 117 (c) 123 (d) 114
  30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
  31. 31.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 17 (b) 16 (c) 15 (d) 23
  32. 32.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  33. 33.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 162 (b) 17 (c) 90 (d) 81
  34. 34.What is the 18th term of the AP 11, 13, 15, 17, …? (a) 45 (b) 34 (c) 36 (d) 47
  35. 35.What is the 23rd term of the AP 2, 11, 20, 29, …? (a) 209 (b) 200 (c) 207 (d) 198
  36. 36.What is the 36th term of the AP 12, 16, 20, 24, …? (a) 156 (b) 152 (c) 140 (d) 144
  37. 37.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 256 (b) 136 (c) 23 (d) 128
  38. 38.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 880 (b) 473 (c) 70 (d) 440
  39. 39.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 33 (b) 31 (c) 41 (d) 32
  40. 40.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 34 (b) 180 (c) 324 (d) 162

Answer key

  1. 249
  2. 53
  3. 729
  4. 42
  5. 55
  6. 21
  7. 20
  8. 300
  9. 81
  10. 24
  11. 38th
  12. 129
  13. 61
  14. 15
  15. 4005
  16. 183
  17. 275
  18. 99
  19. 180
  20. 73
  21. 324
  22. 44
  23. 6
  24. 195
  25. 625
  26. 196
  27. 144
  28. 76
  29. 123
  30. 121
  31. 16
  32. 49
  33. 81
  34. 45
  35. 200
  36. 152
  37. 128
  38. 440
  39. 32
  40. 162

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