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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 78 · 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 40th term of the AP 16, 22, 28, 34, …? (a) 234 (b) 240 (c) 256 (d) 250
  2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 23 (d) 78
  3. 3.What is the 10th term of the AP 19, 28, 37, 46, …? (a) 90 (b) 100 (c) 109 (d) 81
  4. 4.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 496 (c) 512 (d) 1056
  5. 5.What is the 31st term of the AP 19, 27, 35, 43, …? (a) 248 (b) 259 (c) 240 (d) 267
  6. 6.What is the 34th term of the AP 5, 11, 17, 23, …? (a) 204 (b) 198 (c) 203 (d) 209
  7. 7.What is the 17th term of the AP 2, 4, 6, 8, …? (a) 34 (b) 35 (c) 36 (d) 32
  8. 8.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 70 (b) 140 (c) 85 (d) 26
  9. 9.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 588 (c) 294 (d) 312
  10. 10.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 23 (b) 25 (c) 31 (d) 24
  11. 11.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 18 (b) 60 (c) 120 (d) 63
  12. 12.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 40 (c) 12 (d) 45
  13. 13.Which term of the AP 16, 25, 34, 43, … is 232? (a) 27th (b) 25th (c) 26th (d) 24th
  14. 14.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4753 (c) 9506 (d) 4754
  15. 15.What is the 26th term of the AP 1, 4, 7, 10, …? (a) 78 (b) 79 (c) 76 (d) 75
  16. 16.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2048 (c) 4160 (d) 2080
  17. 17.What is the 18th term of the AP 11, 13, 15, 17, …? (a) 45 (b) 47 (c) 36 (d) 34
  18. 18.What is the 40th term of the AP 4, 11, 18, 25, …? (a) 280 (b) 284 (c) 277 (d) 273
  19. 19.What is the 36th term of the AP 4, 12, 20, 28, …? (a) 288 (b) 292 (c) 280 (d) 284
  20. 20.Which term of the AP 12, 17, 22, 27, … is 87? (a) 16th (b) 18th (c) 15th (d) 17th
  21. 21.Which term of the AP 12, 21, 30, 39, … is 273? (a) 32nd (b) 31st (c) 30th (d) 29th
  22. 22.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 228 (b) 420 (c) 34 (d) 210
  23. 23.Which term of the AP 1, 8, 15, 22, … is 78? (a) 14th (b) 12th (c) 11th (d) 13th
  24. 24.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 17 (b) 162 (c) 90 (d) 81
  25. 25.Which term of the AP 15, 17, 19, 21, … is 29? (a) 9th (b) 10th (c) 8th (d) 7th
  26. 26.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 7140 (c) 3528 (d) 3570
  27. 27.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 4830 (c) 2346 (d) 2416
  28. 28.What is the 24th term of the AP 20, 23, 26, 29, …? (a) 92 (b) 89 (c) 69 (d) 72
  29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  30. 30.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 490 (b) 47 (c) 245 (d) 270
  31. 31.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 76 (b) 1032 (c) 552 (d) 516
  32. 32.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 29 (b) 30 (c) 38 (d) 28
  33. 33.What is the 20th term of the AP 1, 5, 9, 13, …? (a) 77 (b) 81 (c) 80 (d) 76
  34. 34.What is the 25th term of the AP 14, 19, 24, 29, …? (a) 125 (b) 134 (c) 139 (d) 120
  35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 552 (d) 45
  36. 36.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 340 (c) 170 (d) 180
  37. 37.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 33 (b) 168 (c) 152 (d) 304
  38. 38.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 240 (b) 21 (c) 130 (d) 120
  39. 39.What is the 19th term of the AP 9, 16, 23, 30, …? (a) 133 (b) 135 (c) 126 (d) 142
  40. 40.What is the 29th term of the AP 19, 27, 35, 43, …? (a) 232 (b) 251 (c) 243 (d) 224

Answer key

  1. 250
  2. 144
  3. 100
  4. 528
  5. 259
  6. 203
  7. 34
  8. 70
  9. 294
  10. 24
  11. 60
  12. 40
  13. 25th
  14. 4753
  15. 76
  16. 2080
  17. 45
  18. 277
  19. 284
  20. 16th
  21. 30th
  22. 210
  23. 12th
  24. 81
  25. 8th
  26. 3570
  27. 2415
  28. 89
  29. 324
  30. 245
  31. 516
  32. 29
  33. 77
  34. 134
  35. 529
  36. 170
  37. 152
  38. 120
  39. 135
  40. 243

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