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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 245 · 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 10 terms of the AP 3, 8, 13, …? (a) 510 (b) 255 (c) 280 (d) 48
  2. 2.Which term of the AP 11, 16, 21, 26, … is 116? (a) 24th (b) 21st (c) 22nd (d) 23rd
  3. 3.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 102 (b) 25 (c) 180 (d) 90
  4. 4.What is the missing term in the AP 20, 23, 26, ?, 32? (a) 32 (b) 28 (c) 29 (d) 30
  5. 5.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3486 (c) 7140 (d) 3570
  6. 6.What is the 13th term of the AP 17, 23, 29, 35, …? (a) 95 (b) 89 (c) 72 (d) 78
  7. 7.What is the 29th term of the AP 16, 19, 22, 25, …? (a) 103 (b) 84 (c) 100 (d) 87
  8. 8.What is the 18th term of the AP 16, 25, 34, 43, …? (a) 169 (b) 162 (c) 178 (d) 153
  9. 9.What is the missing term in the AP 14, 21, 28, ?, 42? (a) 35 (b) 42 (c) 34 (d) 36
  10. 10.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 150 (b) 15 (c) 75 (d) 78
  11. 11.What is the missing term in the AP 13, 16, 19, ?, 25? (a) 21 (b) 25 (c) 23 (d) 22
  12. 12.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 32 (b) 24 (c) 25 (d) 26
  13. 13.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 1332 (c) 648 (d) 666
  14. 14.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 17 (c) 77 (d) 84
  15. 15.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 9 (b) 10 (c) 12 (d) 11
  16. 16.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 10 (b) 9 (c) 17 (d) 8
  17. 17.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 90 (b) 28 (c) 95 (d) 180
  18. 18.What is the 15th term of the AP 4, 9, 14, 19, …? (a) 75 (b) 74 (c) 70 (d) 79
  19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  20. 20.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 171 (d) 153
  21. 21.What is the 34th term of the AP 2, 4, 6, 8, …? (a) 70 (b) 66 (c) 68 (d) 69
  22. 22.What is the 39th term of the AP 17, 22, 27, 32, …? (a) 212 (b) 195 (c) 207 (d) 190
  23. 23.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 27 (b) 32 (c) 28 (d) 29
  24. 24.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
  25. 25.What is the 12th term of the AP 5, 9, 13, 17, …? (a) 44 (b) 49 (c) 48 (d) 53
  26. 26.What is the 29th term of the AP 10, 14, 18, 22, …? (a) 122 (b) 116 (c) 126 (d) 112
  27. 27.What is the 19th term of the AP 7, 9, 11, 13, …? (a) 36 (b) 43 (c) 45 (d) 38
  28. 28.What is the 27th term of the AP 6, 9, 12, 15, …? (a) 78 (b) 84 (c) 81 (d) 87
  29. 29.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 756 (c) 379 (d) 378
  30. 30.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
  31. 31.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 704 (c) 703 (d) 666
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 31 (d) 256
  33. 33.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 126 (b) 63 (c) 13 (d) 66
  34. 34.What is the 23rd term of the AP 2, 6, 10, 14, …? (a) 94 (b) 92 (c) 88 (d) 90
  35. 35.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 9 (b) 8 (c) 11 (d) 10
  36. 36.What is the 23rd term of the AP 20, 22, 24, 26, …? (a) 64 (b) 46 (c) 44 (d) 66
  37. 37.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2702 (c) 2701 (d) 2628
  38. 38.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 21 (b) 25 (c) 23 (d) 22
  39. 39.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
  40. 40.Which term of the AP 17, 22, 27, 32, … is 167? (a) 31st (b) 30th (c) 33rd (d) 32nd

Answer key

  1. 255
  2. 22nd
  3. 90
  4. 29
  5. 3570
  6. 89
  7. 100
  8. 169
  9. 35
  10. 75
  11. 22
  12. 25
  13. 666
  14. 77
  15. 10
  16. 9
  17. 90
  18. 74
  19. 625
  20. 171
  21. 68
  22. 207
  23. 28
  24. 225
  25. 49
  26. 122
  27. 43
  28. 84
  29. 378
  30. 196
  31. 703
  32. 256
  33. 63
  34. 90
  35. 9
  36. 64
  37. 2701
  38. 22
  39. 81
  40. 31st

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