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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 243 · 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 1, 8, 15, 22, … is 85? (a) 14th (b) 13th (c) 12th (d) 15th
  2. 2.Which term of the AP 17, 23, 29, 35, … is 107? (a) 17th (b) 18th (c) 15th (d) 16th
  3. 3.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 192 (b) 372 (c) 186 (d) 21
  4. 4.What is the 13th term of the AP 3, 6, 9, 12, …? (a) 42 (b) 36 (c) 39 (d) 40
  5. 5.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 33 (b) 108 (c) 126 (d) 216
  6. 6.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 352 (b) 176 (c) 26 (d) 187
  7. 7.What is the 38th term of the AP 19, 22, 25, 28, …? (a) 130 (b) 114 (c) 111 (d) 133
  8. 8.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 9120 (c) 4560 (d) 4465
  9. 9.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 300 (c) 600 (d) 276
  10. 10.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 36 (b) 43 (c) 34 (d) 35
  11. 11.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 28 (b) 200 (c) 190 (d) 380
  12. 12.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 72 (b) 66 (c) 132 (d) 16
  13. 13.Which term of the AP 6, 10, 14, 18, … is 94? (a) 22nd (b) 24th (c) 23rd (d) 25th
  14. 14.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 4095 (c) 4050 (d) 8190
  15. 15.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 45 (d) 552
  16. 16.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 13 (b) 70 (c) 140 (d) 71
  17. 17.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 17 (b) 12 (c) 10 (d) 11
  18. 18.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 324 (d) 35
  19. 19.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  20. 20.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 160 (b) 28 (c) 290 (d) 145
  21. 21.What is the 27th term of the AP 13, 15, 17, 19, …? (a) 67 (b) 52 (c) 65 (d) 54
  22. 22.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 9 (b) 11 (c) 13 (d) 10
  23. 23.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 67 (d) 132
  24. 24.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 7 (b) 29 (c) 28 (d) 56
  25. 25.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 10 (b) 19 (c) 11 (d) 9
  26. 26.What is the 16th term of the AP 12, 17, 22, 27, …? (a) 80 (b) 92 (c) 87 (d) 75
  27. 27.What is the 38th term of the AP 4, 6, 8, 10, …? (a) 76 (b) 74 (c) 78 (d) 80
  28. 28.What is the 35th term of the AP 2, 8, 14, 20, …? (a) 212 (b) 206 (c) 204 (d) 210
  29. 29.What is the 35th term of the AP 19, 22, 25, 28, …? (a) 121 (b) 124 (c) 102 (d) 105
  30. 30.What is the 12th term of the AP 1, 5, 9, 13, …? (a) 48 (b) 45 (c) 49 (d) 44
  31. 31.Which term of the AP 5, 8, 11, 14, … is 116? (a) 38th (b) 40th (c) 39th (d) 37th
  32. 32.What is the 35th term of the AP 5, 7, 9, 11, …? (a) 68 (b) 75 (c) 73 (d) 70
  33. 33.What is the 12th term of the AP 6, 14, 22, 30, …? (a) 94 (b) 96 (c) 88 (d) 102
  34. 34.Which term of the AP 17, 26, 35, 44, … is 161? (a) 17th (b) 19th (c) 16th (d) 18th
  35. 35.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
  36. 36.What is the 30th term of the AP 18, 25, 32, 39, …? (a) 228 (b) 210 (c) 221 (d) 203
  37. 37.What is the 15th term of the AP 10, 17, 24, 31, …? (a) 98 (b) 115 (c) 108 (d) 105
  38. 38.What is the 18th term of the AP 1, 4, 7, 10, …? (a) 54 (b) 52 (c) 51 (d) 55
  39. 39.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 1176 (c) 1226 (d) 2450
  40. 40.What is the missing term in the AP 12, 16, 20, ?, 28? (a) 25 (b) 24 (c) 23 (d) 28

Answer key

  1. 13th
  2. 16th
  3. 186
  4. 39
  5. 108
  6. 176
  7. 130
  8. 4560
  9. 300
  10. 35
  11. 190
  12. 66
  13. 23rd
  14. 4095
  15. 529
  16. 70
  17. 11
  18. 324
  19. 576
  20. 145
  21. 65
  22. 10
  23. 66
  24. 28
  25. 10
  26. 87
  27. 78
  28. 206
  29. 121
  30. 45
  31. 38th
  32. 73
  33. 94
  34. 17th
  35. 1035
  36. 221
  37. 108
  38. 52
  39. 1225
  40. 24

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