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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 232 · 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 23rd term of the AP 2, 4, 6, 8, …? (a) 48 (b) 47 (c) 44 (d) 46
  2. 2.What is the 11th term of the AP 1, 7, 13, 19, …? (a) 66 (b) 67 (c) 60 (d) 61
  3. 3.What is the 24th term of the AP 3, 12, 21, 30, …? (a) 216 (b) 219 (c) 210 (d) 207
  4. 4.What is the 28th term of the AP 17, 26, 35, 44, …? (a) 243 (b) 252 (c) 260 (d) 269
  5. 5.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1654 (c) 3306 (d) 1653
  6. 6.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 248 (b) 448 (c) 224 (d) 49
  7. 7.Which term of the AP 16, 22, 28, 34, … is 70? (a) 12th (b) 9th (c) 11th (d) 10th
  8. 8.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4851 (c) 4950 (d) 4951
  9. 9.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 24 (b) 26 (c) 32 (d) 25
  10. 10.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 15 (b) 18 (c) 14 (d) 16
  11. 11.What is the 38th term of the AP 18, 21, 24, 27, …? (a) 111 (b) 129 (c) 114 (d) 132
  12. 12.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 55 (b) 60 (c) 110 (d) 21
  13. 13.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 253 (c) 552 (d) 277
  14. 14.What is the 14th term of the AP 4, 12, 20, 28, …? (a) 116 (b) 104 (c) 108 (d) 112
  15. 15.What is the 11th term of the AP 20, 29, 38, 47, …? (a) 110 (b) 99 (c) 90 (d) 119
  16. 16.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 31 (b) 136 (c) 272 (d) 152
  17. 17.What is the missing term in the AP 14, ?, 18, 20, 22? (a) 18 (b) 17 (c) 16 (d) 15
  18. 18.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 16 (b) 17 (c) 15 (d) 14
  19. 19.What is the missing term in the AP 11, 17, ?, 29, 35? (a) 24 (b) 29 (c) 22 (d) 23
  20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  21. 21.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 170 (b) 90 (c) 27 (d) 85
  22. 22.What is the 10th term of the AP 18, 21, 24, 27, …? (a) 30 (b) 27 (c) 48 (d) 45
  23. 23.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
  24. 24.What is the 33rd term of the AP 14, 23, 32, 41, …? (a) 302 (b) 288 (c) 311 (d) 297
  25. 25.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 242 (b) 122 (c) 16 (d) 121
  26. 26.What is the 16th term of the AP 6, 8, 10, 12, …? (a) 36 (b) 30 (c) 32 (d) 38
  27. 27.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 36 (b) 352 (c) 176 (d) 192
  28. 28.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  29. 29.What is the 29th term of the AP 16, 25, 34, 43, …? (a) 277 (b) 261 (c) 252 (d) 268
  30. 30.Which term of the AP 1, 4, 7, 10, … is 22? (a) 7th (b) 10th (c) 9th (d) 8th
  31. 31.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 24 (b) 31 (c) 23 (d) 22
  32. 32.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 19 (b) 17 (c) 18 (d) 22
  33. 33.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 45 (d) 90
  34. 34.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4608 (c) 9312 (d) 4656
  35. 35.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 210 (b) 27 (c) 119 (d) 105
  36. 36.Which term of the AP 5, 10, 15, 20, … is 170? (a) 35th (b) 33rd (c) 34th (d) 36th
  37. 37.Which term of the AP 18, 24, 30, 36, … is 84? (a) 13th (b) 12th (c) 14th (d) 11th
  38. 38.What is the 13th term of the AP 6, 15, 24, 33, …? (a) 123 (b) 108 (c) 117 (d) 114
  39. 39.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 306 (b) 279 (c) 55 (d) 558
  40. 40.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 272 (c) 136 (d) 128

Answer key

  1. 46
  2. 61
  3. 210
  4. 260
  5. 1653
  6. 224
  7. 10th
  8. 4950
  9. 25
  10. 15
  11. 129
  12. 55
  13. 276
  14. 108
  15. 110
  16. 136
  17. 16
  18. 15
  19. 23
  20. 441
  21. 85
  22. 45
  23. 676
  24. 302
  25. 121
  26. 36
  27. 176
  28. 361
  29. 268
  30. 8th
  31. 23
  32. 18
  33. 81
  34. 4656
  35. 105
  36. 34th
  37. 12th
  38. 114
  39. 279
  40. 136

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