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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 558 · 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 20th term of the AP 6, 14, 22, 30, …? (a) 160 (b) 166 (c) 158 (d) 152
  2. 2.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 18 (b) 16 (c) 17 (d) 22
  3. 3.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 390 (b) 210 (c) 33 (d) 195
  4. 4.What is the sum of all the whole numbers from 1 to 60? (a) 1830 (b) 1770 (c) 1800 (d) 3660
  5. 5.What is the 27th term of the AP 3, 11, 19, 27, …? (a) 208 (b) 211 (c) 219 (d) 216
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 64 (d) 36
  7. 7.What is the missing term in the AP 10, 15, 20, ?, 30? (a) 24 (b) 25 (c) 26 (d) 30
  8. 8.What is the missing term in the AP 17, ?, 33, 41, 49? (a) 26 (b) 33 (c) 24 (d) 25
  9. 9.What is the 38th term of the AP 5, 13, 21, 29, …? (a) 304 (b) 309 (c) 296 (d) 301
  10. 10.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 112 (c) 224 (d) 25
  11. 11.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 196 (b) 26 (c) 98 (d) 112
  12. 12.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 150 (b) 75 (c) 21 (d) 78
  13. 13.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 40 (b) 41 (c) 80 (d) 10
  14. 14.Which term of the AP 3, 9, 15, 21, … is 189? (a) 31st (b) 34th (c) 33rd (d) 32nd
  15. 15.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 576 (d) 300
  16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  17. 17.What is the 40th term of the AP 3, 9, 15, 21, …? (a) 243 (b) 240 (c) 234 (d) 237
  18. 18.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 264 (c) 132 (d) 37
  19. 19.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 4 (b) 6 (c) 5 (d) 7
  20. 20.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 12 (b) 51 (c) 100 (d) 50
  21. 21.Which term of the AP 15, 18, 21, 24, … is 42? (a) 14th (b) 10th (c) 9th (d) 11th
  22. 22.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 11 (b) 13 (c) 12 (d) 14
  23. 23.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 48 (b) 624 (c) 336 (d) 312
  24. 24.What is the 37th term of the AP 15, 19, 23, 27, …? (a) 144 (b) 159 (c) 148 (d) 163
  25. 25.What is the missing term in the AP 6, 11, 16, ?, 26? (a) 20 (b) 26 (c) 22 (d) 21
  26. 26.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 78 (b) 42 (c) 39 (d) 9
  27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
  28. 28.What is the 34th term of the AP 10, 13, 16, 19, …? (a) 102 (b) 112 (c) 109 (d) 99
  29. 29.What is the 30th term of the AP 7, 16, 25, 34, …? (a) 261 (b) 268 (c) 277 (d) 270
  30. 30.What is the 40th term of the AP 14, 16, 18, 20, …? (a) 92 (b) 78 (c) 94 (d) 80
  31. 31.What is the 16th term of the AP 6, 10, 14, 18, …? (a) 60 (b) 70 (c) 66 (d) 64
  32. 32.What is the 18th term of the AP 3, 9, 15, 21, …? (a) 111 (b) 105 (c) 108 (d) 102
  33. 33.What is the 15th term of the AP 4, 8, 12, 16, …? (a) 56 (b) 61 (c) 64 (d) 60
  34. 34.What is the 34th term of the AP 19, 23, 27, 31, …? (a) 136 (b) 151 (c) 132 (d) 155
  35. 35.What is the 12th term of the AP 18, 21, 24, 27, …? (a) 54 (b) 36 (c) 51 (d) 33
  36. 36.What is the 37th term of the AP 19, 23, 27, 31, …? (a) 163 (b) 148 (c) 144 (d) 167
  37. 37.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 828 (b) 414 (c) 444 (d) 62
  38. 38.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 19 (b) 17 (c) 18 (d) 20
  39. 39.Which term of the AP 4, 13, 22, 31, … is 355? (a) 40th (b) 42nd (c) 41st (d) 39th
  40. 40.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 322 (b) 161 (c) 41 (d) 182

Answer key

  1. 158
  2. 17
  3. 195
  4. 1830
  5. 211
  6. 64
  7. 25
  8. 25
  9. 301
  10. 112
  11. 98
  12. 75
  13. 40
  14. 32nd
  15. 576
  16. 400
  17. 237
  18. 132
  19. 5
  20. 50
  21. 10th
  22. 12
  23. 312
  24. 159
  25. 21
  26. 39
  27. 144
  28. 109
  29. 268
  30. 92
  31. 66
  32. 105
  33. 60
  34. 151
  35. 51
  36. 163
  37. 414
  38. 18
  39. 40th
  40. 161

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