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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 393 · 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 14th term of the AP 9, 13, 17, 21, …? (a) 56 (b) 65 (c) 52 (d) 61
  2. 2.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 35 (b) 11 (c) 40 (d) 70
  3. 3.What is the 32nd term of the AP 17, 21, 25, 29, …? (a) 124 (b) 145 (c) 141 (d) 128
  4. 4.Which term of the AP 6, 15, 24, 33, … is 96? (a) 13th (b) 10th (c) 12th (d) 11th
  5. 5.What is the 18th term of the AP 10, 15, 20, 25, …? (a) 95 (b) 85 (c) 90 (d) 100
  6. 6.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1485 (c) 3080 (d) 1540
  7. 7.What is the 34th term of the AP 17, 20, 23, 26, …? (a) 99 (b) 102 (c) 116 (d) 119
  8. 8.What is the 25th term of the AP 13, 19, 25, 31, …? (a) 157 (b) 144 (c) 163 (d) 150
  9. 9.What is the 11th term of the AP 9, 13, 17, 21, …? (a) 49 (b) 40 (c) 44 (d) 53
  10. 10.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 324 (b) 319 (c) 638 (d) 54
  11. 11.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 462 (b) 234 (c) 36 (d) 231
  12. 12.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 374 (c) 187 (d) 27
  13. 13.What is the 26th term of the AP 8, 16, 24, 32, …? (a) 216 (b) 200 (c) 209 (d) 208
  14. 14.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 28 (b) 120 (c) 216 (d) 108
  15. 15.What is the 11th term of the AP 5, 11, 17, 23, …? (a) 65 (b) 66 (c) 60 (d) 71
  16. 16.What is the 30th term of the AP 19, 24, 29, 34, …? (a) 164 (b) 169 (c) 150 (d) 145
  17. 17.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 9 (b) 13 (c) 11 (d) 10
  18. 18.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 32 (b) 185 (c) 200 (d) 370
  19. 19.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 16 (b) 20 (c) 18 (d) 17
  20. 20.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 120 (d) 240
  21. 21.Which term of the AP 2, 9, 16, 23, … is 191? (a) 30th (b) 28th (c) 29th (d) 27th
  22. 22.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 342 (c) 153 (d) 162
  23. 23.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 14 (b) 12 (c) 17 (d) 13
  24. 24.What is the 22nd term of the AP 14, 18, 22, 26, …? (a) 102 (b) 84 (c) 98 (d) 88
  25. 25.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 133 (b) 147 (c) 31 (d) 266
  26. 26.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 207 (b) 378 (c) 37 (d) 189
  27. 27.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 1378 (c) 2756 (d) 1326
  28. 28.What is the 21st term of the AP 15, 20, 25, 30, …? (a) 105 (b) 115 (c) 120 (d) 100
  29. 29.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 39 (b) 30 (c) 32 (d) 31
  30. 30.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 145 (b) 160 (c) 28 (d) 290
  31. 31.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 9 (b) 12 (c) 11 (d) 10
  32. 32.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 6 (b) 4 (c) 5 (d) 9
  33. 33.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 562 (d) 1122
  34. 34.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 196 (d) 210
  35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 441 (d) 462
  36. 36.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
  37. 37.What is the missing term in the AP 2, 10, 18, ?, 34? (a) 26 (b) 25 (c) 34 (d) 27
  38. 38.What is the 21st term of the AP 9, 11, 13, 15, …? (a) 40 (b) 49 (c) 42 (d) 51
  39. 39.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 16 (b) 14 (c) 18 (d) 15
  40. 40.What is the 21st term of the AP 17, 23, 29, 35, …? (a) 120 (b) 143 (c) 126 (d) 137

Answer key

  1. 61
  2. 35
  3. 141
  4. 11th
  5. 95
  6. 1540
  7. 116
  8. 157
  9. 49
  10. 319
  11. 231
  12. 187
  13. 208
  14. 108
  15. 65
  16. 164
  17. 10
  18. 185
  19. 17
  20. 225
  21. 28th
  22. 171
  23. 13
  24. 98
  25. 133
  26. 189
  27. 1378
  28. 115
  29. 31
  30. 145
  31. 10
  32. 5
  33. 561
  34. 196
  35. 441
  36. 484
  37. 26
  38. 49
  39. 15
  40. 137

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