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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 186 · 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 23rd term of the AP 13, 20, 27, 34, …? (a) 167 (b) 174 (c) 154 (d) 161
  2. 2.What is the 31st term of the AP 15, 18, 21, 24, …? (a) 93 (b) 108 (c) 105 (d) 90
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 231 (d) 462
  4. 4.What is the 19th term of the AP 3, 8, 13, 18, …? (a) 98 (b) 95 (c) 90 (d) 93
  5. 5.What is the 24th term of the AP 5, 7, 9, 11, …? (a) 51 (b) 46 (c) 53 (d) 48
  6. 6.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 230 (b) 215 (c) 35 (d) 430
  7. 7.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 102 (b) 51 (c) 11 (d) 54
  8. 8.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 385 (c) 62 (d) 704
  9. 9.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 306 (d) 153
  10. 10.What is the missing term in the AP 10, 13, 16, ?, 22? (a) 22 (b) 18 (c) 19 (d) 20
  11. 11.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 12 (b) 14 (c) 19 (d) 13
  12. 12.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1596 (d) 1654
  13. 13.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2312 (c) 2278 (d) 2346
  14. 14.What is the 15th term of the AP 3, 7, 11, 15, …? (a) 60 (b) 63 (c) 56 (d) 59
  15. 15.What is the missing term in the AP 10, 12, 14, ?, 18? (a) 18 (b) 16 (c) 15 (d) 17
  16. 16.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 65 (c) 68 (d) 130
  17. 17.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  18. 18.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1431 (d) 1432
  19. 19.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 462 (b) 41 (c) 253 (d) 231
  20. 20.What is the 32nd term of the AP 15, 21, 27, 33, …? (a) 207 (b) 192 (c) 186 (d) 201
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 600 (d) 47
  22. 22.What is the 16th term of the AP 5, 9, 13, 17, …? (a) 64 (b) 69 (c) 60 (d) 65
  23. 23.Which term of the AP 2, 9, 16, 23, … is 170? (a) 24th (b) 26th (c) 25th (d) 27th
  24. 24.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 5550 (c) 2701 (d) 2738
  25. 25.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 55 (b) 335 (c) 660 (d) 330
  26. 26.What is the 23rd term of the AP 2, 11, 20, 29, …? (a) 209 (b) 198 (c) 207 (d) 200
  27. 27.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1226 (d) 1225
  28. 28.What is the 16th term of the AP 20, 24, 28, 32, …? (a) 84 (b) 64 (c) 80 (d) 60
  29. 29.What is the 26th term of the AP 6, 14, 22, 30, …? (a) 208 (b) 214 (c) 206 (d) 200
  30. 30.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 200 (b) 100 (c) 110 (d) 19
  31. 31.What is the missing term in the AP 6, 15, ?, 33, 42? (a) 24 (b) 33 (c) 25 (d) 23
  32. 32.What is the 16th term of the AP 2, 9, 16, 23, …? (a) 105 (b) 114 (c) 112 (d) 107
  33. 33.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 342 (d) 171
  34. 34.What is the 18th term of the AP 10, 12, 14, 16, …? (a) 44 (b) 36 (c) 34 (d) 46
  35. 35.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 27 (b) 32 (c) 29 (d) 28
  36. 36.What is the 33rd term of the AP 5, 13, 21, 29, …? (a) 261 (b) 256 (c) 264 (d) 269
  37. 37.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 26 (b) 25 (c) 33 (d) 27
  38. 38.What is the 18th term of the AP 13, 17, 21, 25, …? (a) 81 (b) 72 (c) 68 (d) 85
  39. 39.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 595 (d) 631
  40. 40.What is the missing term in the AP 14, 21, ?, 35, 42? (a) 27 (b) 29 (c) 35 (d) 28

Answer key

  1. 167
  2. 105
  3. 441
  4. 93
  5. 51
  6. 215
  7. 51
  8. 352
  9. 289
  10. 19
  11. 13
  12. 1653
  13. 2346
  14. 59
  15. 16
  16. 65
  17. 36
  18. 1431
  19. 231
  20. 201
  21. 576
  22. 65
  23. 25th
  24. 2775
  25. 330
  26. 200
  27. 1225
  28. 80
  29. 206
  30. 100
  31. 24
  32. 107
  33. 324
  34. 44
  35. 28
  36. 261
  37. 26
  38. 81
  39. 630
  40. 28

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