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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 171 · 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 17th term of the AP 19, 25, 31, 37, …? (a) 121 (b) 115 (c) 96 (d) 102
  2. 2.Which term of the AP 7, 10, 13, 16, … is 100? (a) 34th (b) 33rd (c) 31st (d) 32nd
  3. 3.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 600 (c) 300 (d) 276
  4. 4.What is the 30th term of the AP 9, 17, 25, 33, …? (a) 241 (b) 232 (c) 240 (d) 249
  5. 5.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 27 (b) 26 (c) 28 (d) 34
  6. 6.What is the 15th term of the AP 17, 20, 23, 26, …? (a) 59 (b) 45 (c) 62 (d) 42
  7. 7.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 33 (b) 34 (c) 35 (d) 41
  8. 8.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 168 (b) 34 (c) 308 (d) 154
  9. 9.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 191 (c) 380 (d) 190
  10. 10.What is the 22nd term of the AP 4, 9, 14, 19, …? (a) 110 (b) 114 (c) 105 (d) 109
  11. 11.Which term of the AP 13, 18, 23, 28, … is 178? (a) 35th (b) 33rd (c) 36th (d) 34th
  12. 12.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 144 (d) 78
  13. 13.Which term of the AP 12, 17, 22, 27, … is 77? (a) 16th (b) 15th (c) 14th (d) 13th
  14. 14.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 184 (b) 44 (c) 368 (d) 208
  15. 15.What is the 29th term of the AP 11, 13, 15, 17, …? (a) 58 (b) 56 (c) 67 (d) 69
  16. 16.Which term of the AP 20, 29, 38, 47, … is 218? (a) 25th (b) 23rd (c) 24th (d) 22nd
  17. 17.What is the 29th term of the AP 16, 23, 30, 37, …? (a) 212 (b) 203 (c) 219 (d) 196
  18. 18.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  19. 19.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 132 (c) 21 (d) 121
  20. 20.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 336 (b) 180 (c) 168 (d) 25
  21. 21.What is the 33rd term of the AP 12, 14, 16, 18, …? (a) 78 (b) 64 (c) 66 (d) 76
  22. 22.What is the 10th term of the AP 12, 18, 24, 30, …? (a) 66 (b) 60 (c) 54 (d) 72
  23. 23.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 127 (b) 252 (c) 126 (d) 18
  24. 24.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 68 (b) 418 (c) 836 (d) 451
  25. 25.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 44 (b) 35 (c) 36 (d) 37
  26. 26.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 560 (b) 46 (c) 280 (d) 300
  27. 27.What is the 15th term of the AP 18, 21, 24, 27, …? (a) 42 (b) 45 (c) 63 (d) 60
  28. 28.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 16 (b) 14 (c) 18 (d) 15
  29. 29.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 55 (b) 58 (c) 110 (d) 17
  30. 30.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 4950 (c) 10100 (d) 5000
  31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  32. 32.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 23 (b) 17 (c) 18 (d) 19
  33. 33.Which term of the AP 17, 24, 31, 38, … is 262? (a) 36th (b) 37th (c) 38th (d) 35th
  34. 34.What is the 38th term of the AP 4, 8, 12, 16, …? (a) 148 (b) 152 (c) 153 (d) 156
  35. 35.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 380 (b) 28 (c) 200 (d) 190
  36. 36.What is the missing term in the AP 17, 25, 33, ?, 49? (a) 49 (b) 42 (c) 41 (d) 40
  37. 37.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 100 (b) 16 (c) 53 (d) 50
  38. 38.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 135 (b) 270 (c) 144 (d) 23
  39. 39.What is the 16th term of the AP 13, 18, 23, 28, …? (a) 88 (b) 80 (c) 75 (d) 93
  40. 40.What is the 23rd term of the AP 8, 16, 24, 32, …? (a) 185 (b) 176 (c) 192 (d) 184

Answer key

  1. 115
  2. 32nd
  3. 300
  4. 241
  5. 27
  6. 59
  7. 34
  8. 154
  9. 190
  10. 109
  11. 34th
  12. 144
  13. 14th
  14. 184
  15. 67
  16. 23rd
  17. 212
  18. 2556
  19. 121
  20. 168
  21. 76
  22. 66
  23. 126
  24. 418
  25. 36
  26. 280
  27. 60
  28. 15
  29. 55
  30. 5050
  31. 81
  32. 18
  33. 36th
  34. 152
  35. 190
  36. 41
  37. 50
  38. 135
  39. 88
  40. 184

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