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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 304 · 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 8 terms of the AP 9, 15, 21, …? (a) 51 (b) 480 (c) 264 (d) 240
  2. 2.Which term of the AP 12, 21, 30, 39, … is 282? (a) 31st (b) 32nd (c) 33rd (d) 30th
  3. 3.What is the 23rd term of the AP 2, 6, 10, 14, …? (a) 90 (b) 92 (c) 94 (d) 88
  4. 4.What is the missing term in the AP 18, ?, 28, 33, 38? (a) 24 (b) 22 (c) 28 (d) 23
  5. 5.What is the 29th term of the AP 7, 12, 17, 22, …? (a) 140 (b) 147 (c) 152 (d) 145
  6. 6.What is the 39th term of the AP 16, 21, 26, 31, …? (a) 195 (b) 190 (c) 206 (d) 211
  7. 7.What is the 23rd term of the AP 9, 17, 25, 33, …? (a) 185 (b) 193 (c) 176 (d) 184
  8. 8.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 266 (c) 154 (d) 133
  9. 9.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 66 (c) 78 (d) 72
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 306 (d) 153
  11. 11.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 40 (b) 39 (c) 49 (d) 41
  12. 12.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 50 (b) 100 (c) 53 (d) 16
  13. 13.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 171 (c) 380 (d) 191
  14. 14.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 98 (c) 210 (d) 91
  15. 15.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 351 (c) 756 (d) 378
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  17. 17.What is the missing term in the AP 11, 18, 25, ?, 39? (a) 33 (b) 31 (c) 39 (d) 32
  18. 18.What is the 22nd term of the AP 8, 10, 12, 14, …? (a) 52 (b) 50 (c) 44 (d) 42
  19. 19.What is the 18th term of the AP 4, 13, 22, 31, …? (a) 166 (b) 162 (c) 157 (d) 153
  20. 20.What is the 10th term of the AP 14, 23, 32, 41, …? (a) 81 (b) 90 (c) 95 (d) 104
  21. 21.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 108 (b) 216 (c) 120 (d) 28
  22. 22.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 168 (c) 336 (d) 39
  23. 23.Which term of the AP 15, 18, 21, 24, … is 48? (a) 11th (b) 13th (c) 12th (d) 16th
  24. 24.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 630 (c) 595 (d) 631
  25. 25.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 253 (c) 242 (d) 231
  26. 26.What is the 32nd term of the AP 15, 23, 31, 39, …? (a) 248 (b) 263 (c) 271 (d) 256
  27. 27.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 143 (b) 264 (c) 132 (d) 22
  28. 28.What is the 26th term of the AP 20, 29, 38, 47, …? (a) 254 (b) 245 (c) 225 (d) 234
  29. 29.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 130 (c) 70 (d) 65
  30. 30.What is the 12th term of the AP 14, 19, 24, 29, …? (a) 55 (b) 69 (c) 60 (d) 74
  31. 31.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 297 (b) 594 (c) 57 (d) 324
  32. 32.What is the 22nd term of the AP 6, 15, 24, 33, …? (a) 198 (b) 204 (c) 195 (d) 189
  33. 33.What is the 28th term of the AP 16, 21, 26, 31, …? (a) 140 (b) 156 (c) 151 (d) 135
  34. 34.What is the 15th term of the AP 1, 7, 13, 19, …? (a) 84 (b) 90 (c) 91 (d) 85
  35. 35.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 19 (b) 17 (c) 18 (d) 26
  36. 36.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 24 (b) 22 (c) 20 (d) 21
  37. 37.What is the 11th term of the AP 5, 11, 17, 23, …? (a) 60 (b) 71 (c) 65 (d) 66
  38. 38.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 98 (b) 91 (c) 182 (d) 19
  39. 39.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 11 (b) 13 (c) 14 (d) 12
  40. 40.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 11 (b) 13 (c) 21 (d) 12

Answer key

  1. 240
  2. 31st
  3. 90
  4. 23
  5. 147
  6. 206
  7. 185
  8. 133
  9. 78
  10. 289
  11. 40
  12. 50
  13. 190
  14. 105
  15. 378
  16. 441
  17. 32
  18. 50
  19. 157
  20. 95
  21. 108
  22. 168
  23. 12th
  24. 630
  25. 253
  26. 263
  27. 132
  28. 245
  29. 65
  30. 69
  31. 297
  32. 195
  33. 151
  34. 85
  35. 18
  36. 21
  37. 65
  38. 91
  39. 12
  40. 12

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