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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 141 · 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 sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  2. 2.What is the 16th term of the AP 12, 18, 24, 30, …? (a) 96 (b) 90 (c) 102 (d) 108
  3. 3.What is the 29th term of the AP 2, 4, 6, 8, …? (a) 58 (b) 60 (c) 59 (d) 56
  4. 4.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 9 (b) 13 (c) 10 (d) 11
  5. 5.What is the 11th term of the AP 3, 9, 15, 21, …? (a) 63 (b) 60 (c) 66 (d) 69
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  7. 7.What is the 32nd term of the AP 20, 23, 26, 29, …? (a) 96 (b) 113 (c) 116 (d) 93
  8. 8.Which term of the AP 17, 21, 25, 29, … is 157? (a) 35th (b) 36th (c) 38th (d) 37th
  9. 9.What is the 28th term of the AP 1, 8, 15, 22, …? (a) 190 (b) 196 (c) 189 (d) 197
  10. 10.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 1953 (c) 3906 (d) 1922
  11. 11.What is the 13th term of the AP 17, 24, 31, 38, …? (a) 84 (b) 91 (c) 108 (d) 101
  12. 12.What is the 15th term of the AP 5, 9, 13, 17, …? (a) 65 (b) 60 (c) 56 (d) 61
  13. 13.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 784 (d) 812
  14. 14.What is the 33rd term of the AP 20, 28, 36, 44, …? (a) 284 (b) 276 (c) 264 (d) 256
  15. 15.Which term of the AP 4, 7, 10, 13, … is 109? (a) 36th (b) 35th (c) 38th (d) 37th
  16. 16.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 32 (b) 24 (c) 25 (d) 26
  17. 17.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 231 (c) 232 (d) 462
  18. 18.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 578 (c) 595 (d) 1190
  19. 19.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 91 (b) 98 (c) 19 (d) 182
  20. 20.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 648 (c) 666 (d) 630
  21. 21.What is the 36th term of the AP 2, 8, 14, 20, …? (a) 210 (b) 212 (c) 216 (d) 218
  22. 22.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 325 (d) 300
  23. 23.Which term of the AP 16, 24, 32, 40, … is 248? (a) 30th (b) 31st (c) 29th (d) 32nd
  24. 24.Which term of the AP 14, 17, 20, 23, … is 53? (a) 15th (b) 13th (c) 14th (d) 16th
  25. 25.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 37 (b) 470 (c) 250 (d) 235
  26. 26.What is the 17th term of the AP 11, 15, 19, 23, …? (a) 68 (b) 79 (c) 75 (d) 64
  27. 27.What is the 13th term of the AP 12, 19, 26, 33, …? (a) 96 (b) 91 (c) 103 (d) 84
  28. 28.What is the 22nd term of the AP 9, 12, 15, 18, …? (a) 66 (b) 72 (c) 75 (d) 63
  29. 29.What is the 25th term of the AP 19, 27, 35, 43, …? (a) 192 (b) 219 (c) 200 (d) 211
  30. 30.Which term of the AP 10, 16, 22, 28, … is 226? (a) 39th (b) 38th (c) 37th (d) 36th
  31. 31.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 153 (b) 144 (c) 24 (d) 288
  32. 32.What is the 20th term of the AP 6, 13, 20, 27, …? (a) 133 (b) 146 (c) 140 (d) 139
  33. 33.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 3080 (c) 1540 (d) 1485
  34. 34.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 34 (b) 41 (c) 36 (d) 35
  35. 35.What is the 26th term of the AP 1, 9, 17, 25, …? (a) 209 (b) 208 (c) 200 (d) 201
  36. 36.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  37. 37.Which term of the AP 3, 11, 19, 27, … is 115? (a) 16th (b) 15th (c) 14th (d) 17th
  38. 38.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 186 (b) 23 (c) 93 (d) 102
  39. 39.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 324 (d) 171
  40. 40.What is the 35th term of the AP 7, 15, 23, 31, …? (a) 272 (b) 287 (c) 280 (d) 279

Answer key

  1. 36
  2. 102
  3. 58
  4. 10
  5. 63
  6. 64
  7. 113
  8. 36th
  9. 190
  10. 1953
  11. 101
  12. 61
  13. 784
  14. 276
  15. 36th
  16. 25
  17. 231
  18. 595
  19. 91
  20. 666
  21. 212
  22. 325
  23. 30th
  24. 14th
  25. 235
  26. 75
  27. 96
  28. 72
  29. 211
  30. 37th
  31. 144
  32. 139
  33. 1540
  34. 35
  35. 201
  36. 225
  37. 15th
  38. 93
  39. 324
  40. 279

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