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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 720 · 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 17, 23, 29, 35, … is 131? (a) 19th (b) 21st (c) 22nd (d) 20th
  2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 49 (d) 13
  3. 3.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 253 (c) 242 (d) 506
  4. 4.Which term of the AP 4, 9, 14, 19, … is 64? (a) 14th (b) 12th (c) 15th (d) 13th
  5. 5.Which term of the AP 12, 17, 22, 27, … is 197? (a) 39th (b) 40th (c) 38th (d) 37th
  6. 6.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 7656 (c) 3829 (d) 3828
  7. 7.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3916 (c) 3872 (d) 7832
  8. 8.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 4 (b) 2 (c) 5 (d) 3
  9. 9.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 722 (c) 1482 (d) 703
  10. 10.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 70 (c) 65 (d) 130
  11. 11.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 351 (c) 378 (d) 756
  12. 12.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 87 (b) 84 (c) 21 (d) 168
  13. 13.What is the 22nd term of the AP 5, 8, 11, 14, …? (a) 68 (b) 63 (c) 71 (d) 66
  14. 14.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 306 (b) 333 (c) 58 (d) 612
  15. 15.Which term of the AP 2, 4, 6, 8, … is 48? (a) 26th (b) 24th (c) 23rd (d) 25th
  16. 16.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 8 (b) 9 (c) 7 (d) 6
  17. 17.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 38 (b) 39 (c) 40 (d) 48
  18. 18.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 37 (b) 45 (c) 35 (d) 36
  19. 19.What is the 40th term of the AP 10, 15, 20, 25, …? (a) 205 (b) 210 (c) 200 (d) 195
  20. 20.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 18 (b) 14 (c) 12 (d) 13
  21. 21.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  22. 22.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 1800 (c) 1830 (d) 3660
  23. 23.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 8 (b) 36 (c) 40 (d) 72
  24. 24.What is the sum of all the whole numbers from 1 to 79? (a) 6320 (b) 3160 (c) 3161 (d) 3081
  25. 25.What is the 29th term of the AP 14, 16, 18, 20, …? (a) 72 (b) 56 (c) 58 (d) 70
  26. 26.Which term of the AP 10, 18, 26, 34, … is 322? (a) 42nd (b) 39th (c) 41st (d) 40th
  27. 27.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
  28. 28.Which term of the AP 20, 22, 24, 26, … is 44? (a) 22nd (b) 12th (c) 14th (d) 13th
  29. 29.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2080 (c) 2145 (d) 2146
  30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  31. 31.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 208 (b) 368 (c) 184 (d) 44
  32. 32.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 44 (b) 54 (c) 45 (d) 46
  33. 33.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 234 (b) 462 (c) 36 (d) 231
  34. 34.What is the 18th term of the AP 15, 18, 21, 24, …? (a) 54 (b) 66 (c) 69 (d) 51
  35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 42 (d) 11
  36. 36.What is the 38th term of the AP 10, 18, 26, 34, …? (a) 314 (b) 304 (c) 306 (d) 296
  37. 37.What is the 24th term of the AP 9, 11, 13, 15, …? (a) 48 (b) 55 (c) 46 (d) 57
  38. 38.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 260 (b) 235 (c) 46 (d) 470
  39. 39.What is the 15th term of the AP 3, 8, 13, 18, …? (a) 78 (b) 70 (c) 75 (d) 73
  40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15

Answer key

  1. 20th
  2. 49
  3. 253
  4. 13th
  5. 38th
  6. 3828
  7. 3916
  8. 3
  9. 741
  10. 65
  11. 378
  12. 84
  13. 68
  14. 306
  15. 24th
  16. 7
  17. 39
  18. 36
  19. 205
  20. 13
  21. 144
  22. 1830
  23. 36
  24. 3160
  25. 70
  26. 40th
  27. 361
  28. 13th
  29. 2145
  30. 121
  31. 184
  32. 45
  33. 231
  34. 66
  35. 36
  36. 306
  37. 55
  38. 235
  39. 73
  40. 64

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