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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 370 · 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 29th term of the AP 4, 6, 8, 10, …? (a) 56 (b) 58 (c) 60 (d) 62
  2. 2.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 22 (b) 30 (c) 23 (d) 21
  3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
  4. 4.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 1892 (c) 903 (d) 947
  5. 5.Which term of the AP 15, 18, 21, 24, … is 111? (a) 32nd (b) 34th (c) 37th (d) 33rd
  6. 6.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 140 (b) 280 (c) 154 (d) 32
  7. 7.What is the 27th term of the AP 20, 27, 34, 41, …? (a) 202 (b) 189 (c) 209 (d) 182
  8. 8.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 25 (b) 26 (c) 31 (d) 27
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 182 (d) 25
  10. 10.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 23 (b) 21 (c) 22 (d) 31
  11. 11.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 61 (b) 340 (c) 680 (d) 370
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 42 (d) 21
  13. 13.What is the 37th term of the AP 6, 10, 14, 18, …? (a) 144 (b) 148 (c) 154 (d) 150
  14. 14.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 21 (b) 242 (c) 121 (d) 132
  15. 15.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 28 (b) 20 (c) 19 (d) 21
  16. 16.What is the 28th term of the AP 17, 26, 35, 44, …? (a) 260 (b) 243 (c) 252 (d) 269
  17. 17.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 4830 (c) 2346 (d) 2415
  18. 18.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 186 (c) 192 (d) 21
  19. 19.Which term of the AP 20, 29, 38, 47, … is 254? (a) 29th (b) 26th (c) 28th (d) 27th
  20. 20.What is the 21st term of the AP 5, 13, 21, 29, …? (a) 173 (b) 168 (c) 160 (d) 165
  21. 21.What is the missing term in the AP 16, 21, 26, ?, 36? (a) 36 (b) 30 (c) 31 (d) 32
  22. 22.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 37 (c) 132 (d) 264
  23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  24. 24.What is the 22nd term of the AP 5, 9, 13, 17, …? (a) 93 (b) 88 (c) 84 (d) 89
  25. 25.What is the 32nd term of the AP 3, 10, 17, 24, …? (a) 217 (b) 224 (c) 220 (d) 227
  26. 26.Which term of the AP 6, 13, 20, 27, … is 272? (a) 40th (b) 38th (c) 41st (d) 39th
  27. 27.What is the 29th term of the AP 4, 10, 16, 22, …? (a) 172 (b) 178 (c) 168 (d) 174
  28. 28.What is the 26th term of the AP 15, 17, 19, 21, …? (a) 67 (b) 50 (c) 65 (d) 52
  29. 29.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 516 (b) 960 (c) 73 (d) 480
  30. 30.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 9506 (c) 4753 (d) 4754
  31. 31.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 306 (b) 156 (c) 29 (d) 153
  32. 32.What is the 15th term of the AP 6, 11, 16, 21, …? (a) 75 (b) 76 (c) 70 (d) 81
  33. 33.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 8372 (c) 4186 (d) 4187
  34. 34.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4371 (c) 8930 (d) 4465
  35. 35.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 39 (b) 29 (c) 30 (d) 31
  36. 36.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2145 (c) 2211 (d) 2178
  37. 37.What is the 18th term of the AP 19, 24, 29, 34, …? (a) 85 (b) 109 (c) 90 (d) 104
  38. 38.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 57 (d) 870
  39. 39.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 648 (b) 348 (c) 49 (d) 324
  40. 40.What is the 28th term of the AP 5, 14, 23, 32, …? (a) 252 (b) 243 (c) 257 (d) 248

Answer key

  1. 60
  2. 22
  3. 81
  4. 946
  5. 33rd
  6. 140
  7. 202
  8. 26
  9. 169
  10. 22
  11. 340
  12. 36
  13. 150
  14. 121
  15. 20
  16. 260
  17. 2415
  18. 186
  19. 27th
  20. 165
  21. 31
  22. 132
  23. 729
  24. 89
  25. 220
  26. 39th
  27. 172
  28. 65
  29. 480
  30. 4753
  31. 153
  32. 76
  33. 4186
  34. 4465
  35. 30
  36. 2211
  37. 104
  38. 841
  39. 324
  40. 248

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