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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 376 · 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 15, 19, 23, 27, … is 87? (a) 18th (b) 21st (c) 19th (d) 20th
  2. 2.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 432 (b) 804 (c) 61 (d) 402
  3. 3.What is the 38th term of the AP 5, 8, 11, 14, …? (a) 116 (b) 111 (c) 114 (d) 119
  4. 4.What is the 38th term of the AP 5, 10, 15, 20, …? (a) 190 (b) 195 (c) 191 (d) 185
  5. 5.What is the 10th term of the AP 17, 21, 25, 29, …? (a) 36 (b) 40 (c) 57 (d) 53
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  7. 7.Which term of the AP 5, 10, 15, 20, … is 200? (a) 40th (b) 41st (c) 42nd (d) 39th
  8. 8.Which term of the AP 6, 15, 24, 33, … is 96? (a) 13th (b) 10th (c) 12th (d) 11th
  9. 9.What is the 29th term of the AP 13, 17, 21, 25, …? (a) 129 (b) 125 (c) 112 (d) 116
  10. 10.What is the missing term in the AP 15, 19, ?, 27, 31? (a) 24 (b) 23 (c) 27 (d) 22
  11. 11.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3528 (c) 7140 (d) 3570
  12. 12.What is the 40th term of the AP 4, 6, 8, 10, …? (a) 84 (b) 82 (c) 78 (d) 80
  13. 13.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 9 (b) 14 (c) 7 (d) 8
  14. 14.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 15 (c) 63 (d) 70
  15. 15.What is the missing term in the AP 13, 16, 19, ?, 25? (a) 21 (b) 25 (c) 22 (d) 23
  16. 16.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 172 (b) 192 (c) 39 (d) 344
  17. 17.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 16 (c) 65 (d) 60
  18. 18.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 15 (b) 13 (c) 14 (d) 20
  19. 19.What is the 28th term of the AP 14, 17, 20, 23, …? (a) 84 (b) 81 (c) 95 (d) 98
  20. 20.Which term of the AP 20, 22, 24, 26, … is 36? (a) 8th (b) 9th (c) 18th (d) 10th
  21. 21.What is the 36th term of the AP 1, 5, 9, 13, …? (a) 140 (b) 144 (c) 145 (d) 141
  22. 22.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 99 (c) 198 (d) 108
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  24. 24.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 136 (c) 154 (d) 153
  25. 25.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3828 (d) 3916
  26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  27. 27.What is the 25th term of the AP 3, 12, 21, 30, …? (a) 225 (b) 219 (c) 228 (d) 216
  28. 28.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1035 (c) 1081 (d) 1058
  29. 29.What is the 22nd term of the AP 8, 10, 12, 14, …? (a) 50 (b) 52 (c) 44 (d) 42
  30. 30.What is the 23rd term of the AP 19, 28, 37, 46, …? (a) 226 (b) 198 (c) 207 (d) 217
  31. 31.What is the 16th term of the AP 8, 12, 16, 20, …? (a) 64 (b) 68 (c) 60 (d) 72
  32. 32.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 69 (b) 138 (c) 19 (d) 78
  33. 33.What is the 28th term of the AP 6, 15, 24, 33, …? (a) 249 (b) 252 (c) 258 (d) 243
  34. 34.Which term of the AP 9, 16, 23, 30, … is 275? (a) 38th (b) 40th (c) 41st (d) 39th
  35. 35.What is the 19th term of the AP 14, 23, 32, 41, …? (a) 176 (b) 171 (c) 185 (d) 162
  36. 36.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
  37. 37.Which term of the AP 20, 23, 26, 29, … is 137? (a) 40th (b) 39th (c) 41st (d) 42nd
  38. 38.What is the 27th term of the AP 15, 17, 19, 21, …? (a) 54 (b) 52 (c) 67 (d) 69
  39. 39.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 32 (b) 30 (c) 37 (d) 31
  40. 40.What is the 26th term of the AP 3, 12, 21, 30, …? (a) 237 (b) 225 (c) 234 (d) 228

Answer key

  1. 19th
  2. 402
  3. 116
  4. 190
  5. 53
  6. 64
  7. 40th
  8. 11th
  9. 125
  10. 23
  11. 3570
  12. 82
  13. 8
  14. 63
  15. 22
  16. 172
  17. 60
  18. 14
  19. 95
  20. 9th
  21. 141
  22. 99
  23. 100
  24. 153
  25. 3916
  26. 121
  27. 219
  28. 1081
  29. 50
  30. 217
  31. 68
  32. 69
  33. 249
  34. 39th
  35. 176
  36. 324
  37. 40th
  38. 67
  39. 31
  40. 228

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