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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 419 · 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 missing term in the AP 18, 26, ?, 42, 50? (a) 34 (b) 42 (c) 33 (d) 35
  2. 2.Which term of the AP 6, 14, 22, 30, … is 70? (a) 11th (b) 9th (c) 10th (d) 8th
  3. 3.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 27 (b) 102 (c) 87 (d) 174
  4. 4.What is the 18th term of the AP 8, 16, 24, 32, …? (a) 136 (b) 145 (c) 152 (d) 144
  5. 5.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 240 (b) 480 (c) 252 (d) 31
  6. 6.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 132 (b) 117 (c) 32 (d) 234
  7. 7.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 726 (b) 63 (c) 363 (d) 396
  8. 8.What is the missing term in the AP 9, 18, ?, 36, 45? (a) 26 (b) 27 (c) 36 (d) 28
  9. 9.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 450 (b) 252 (c) 225 (d) 49
  10. 10.What is the 21st term of the AP 20, 23, 26, 29, …? (a) 80 (b) 63 (c) 60 (d) 83
  11. 11.What is the 23rd term of the AP 6, 9, 12, 15, …? (a) 69 (b) 72 (c) 75 (d) 66
  12. 12.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 31 (b) 32 (c) 30 (d) 39
  13. 13.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 392 (c) 812 (d) 406
  14. 14.What is the 22nd term of the AP 16, 21, 26, 31, …? (a) 126 (b) 121 (c) 105 (d) 110
  15. 15.What is the 23rd term of the AP 3, 7, 11, 15, …? (a) 95 (b) 92 (c) 91 (d) 88
  16. 16.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 253 (b) 43 (c) 506 (d) 275
  17. 17.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 110 (b) 200 (c) 100 (d) 19
  18. 18.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 5256 (c) 2556 (d) 2628
  19. 19.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 22 (b) 70 (c) 80 (d) 140
  20. 20.What is the 13th term of the AP 11, 15, 19, 23, …? (a) 52 (b) 59 (c) 48 (d) 63
  21. 21.What is the 22nd term of the AP 10, 15, 20, 25, …? (a) 115 (b) 105 (c) 110 (d) 120
  22. 22.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 528 (c) 264 (d) 267
  23. 23.What is the 19th term of the AP 19, 25, 31, 37, …? (a) 114 (b) 127 (c) 108 (d) 133
  24. 24.Which term of the AP 10, 12, 14, 16, … is 68? (a) 31st (b) 34th (c) 30th (d) 29th
  25. 25.Which term of the AP 3, 8, 13, 18, … is 103? (a) 21st (b) 22nd (c) 20th (d) 23rd
  26. 26.What is the sum of all the whole numbers from 1 to 84? (a) 3570 (b) 7140 (c) 3486 (d) 3528
  27. 27.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 130 (c) 68 (d) 65
  28. 28.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 784 (d) 406
  29. 29.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 50 (b) 7 (c) 26 (d) 25
  30. 30.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  31. 31.What is the 12th term of the AP 17, 22, 27, 32, …? (a) 72 (b) 77 (c) 60 (d) 55
  32. 32.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 65 (c) 130 (d) 25
  33. 33.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 210 (b) 420 (c) 39 (d) 230
  34. 34.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 529 (d) 552
  35. 35.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  36. 36.What is the 36th term of the AP 20, 26, 32, 38, …? (a) 216 (b) 210 (c) 236 (d) 230
  37. 37.What is the 32nd term of the AP 4, 7, 10, 13, …? (a) 97 (b) 93 (c) 96 (d) 100
  38. 38.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4050 (c) 4005 (d) 4095
  39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  40. 40.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 378 (b) 194 (c) 41 (d) 189

Answer key

  1. 34
  2. 9th
  3. 87
  4. 144
  5. 240
  6. 117
  7. 363
  8. 27
  9. 225
  10. 80
  11. 72
  12. 31
  13. 406
  14. 121
  15. 91
  16. 253
  17. 100
  18. 2628
  19. 70
  20. 59
  21. 115
  22. 264
  23. 127
  24. 30th
  25. 21st
  26. 3570
  27. 65
  28. 784
  29. 25
  30. 36
  31. 72
  32. 65
  33. 210
  34. 529
  35. 841
  36. 230
  37. 97
  38. 4095
  39. 25
  40. 189

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