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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 258 · 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 all the whole numbers from 1 to 85? (a) 7310 (b) 3656 (c) 3570 (d) 3655
  2. 2.What is the 28th term of the AP 2, 7, 12, 17, …? (a) 140 (b) 142 (c) 137 (d) 135
  3. 3.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 275 (b) 43 (c) 506 (d) 253
  4. 4.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 1640 (c) 820 (d) 800
  5. 5.What is the 15th term of the AP 15, 19, 23, 27, …? (a) 60 (b) 75 (c) 56 (d) 71
  6. 6.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 6 (b) 5 (c) 8 (d) 4
  7. 7.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 13 (b) 8 (c) 7 (d) 9
  8. 8.What is the 26th term of the AP 12, 14, 16, 18, …? (a) 50 (b) 62 (c) 64 (d) 52
  9. 9.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 42 (d) 36
  10. 10.What is the 16th term of the AP 3, 11, 19, 27, …? (a) 131 (b) 128 (c) 123 (d) 120
  11. 11.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 220 (b) 111 (c) 15 (d) 110
  12. 12.Which term of the AP 12, 17, 22, 27, … is 162? (a) 30th (b) 31st (c) 32nd (d) 33rd
  13. 13.Which term of the AP 16, 18, 20, 22, … is 54? (a) 20th (b) 19th (c) 27th (d) 21st
  14. 14.What is the 21st term of the AP 1, 6, 11, 16, …? (a) 101 (b) 106 (c) 105 (d) 100
  15. 15.Which term of the AP 13, 19, 25, 31, … is 229? (a) 39th (b) 38th (c) 37th (d) 36th
  16. 16.What is the 29th term of the AP 8, 10, 12, 14, …? (a) 58 (b) 66 (c) 64 (d) 56
  17. 17.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 3828 (c) 3741 (d) 7656
  18. 18.Which term of the AP 19, 21, 23, 25, … is 51? (a) 17th (b) 16th (c) 18th (d) 19th
  19. 19.What is the 40th term of the AP 12, 15, 18, 21, …? (a) 132 (b) 120 (c) 117 (d) 129
  20. 20.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 504 (b) 52 (c) 279 (d) 252
  21. 21.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 12 (b) 17 (c) 14 (d) 13
  22. 22.Which term of the AP 3, 7, 11, 15, … is 151? (a) 37th (b) 38th (c) 40th (d) 39th
  23. 23.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 105 (b) 100 (c) 200 (d) 30
  24. 24.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 35 (b) 28 (c) 29 (d) 30
  25. 25.What is the 30th term of the AP 19, 26, 33, 40, …? (a) 229 (b) 222 (c) 210 (d) 203
  26. 26.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 17 (b) 15 (c) 16 (d) 23
  27. 27.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 435 (c) 465 (d) 450
  28. 28.What is the 28th term of the AP 6, 15, 24, 33, …? (a) 243 (b) 252 (c) 249 (d) 258
  29. 29.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1225 (c) 1226 (d) 1176
  30. 30.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 16 (b) 15 (c) 25 (d) 17
  31. 31.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 35 (c) 40 (d) 70
  32. 32.What is the 28th term of the AP 2, 9, 16, 23, …? (a) 189 (b) 198 (c) 196 (d) 191
  33. 33.What is the 34th term of the AP 4, 7, 10, 13, …? (a) 106 (b) 102 (c) 103 (d) 99
  34. 34.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 45 (c) 11 (d) 46
  35. 35.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 182 (b) 25 (c) 105 (d) 91
  36. 36.What is the 24th term of the AP 4, 13, 22, 31, …? (a) 207 (b) 220 (c) 211 (d) 216
  37. 37.Which term of the AP 5, 10, 15, 20, … is 80? (a) 18th (b) 16th (c) 17th (d) 15th
  38. 38.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 19 (b) 12 (c) 13 (d) 14
  39. 39.Which term of the AP 1, 10, 19, 28, … is 316? (a) 35th (b) 38th (c) 37th (d) 36th
  40. 40.Which term of the AP 1, 5, 9, 13, … is 89? (a) 22nd (b) 24th (c) 25th (d) 23rd

Answer key

  1. 3655
  2. 137
  3. 253
  4. 820
  5. 71
  6. 5
  7. 8
  8. 62
  9. 36
  10. 123
  11. 110
  12. 31st
  13. 20th
  14. 101
  15. 37th
  16. 64
  17. 3828
  18. 17th
  19. 129
  20. 252
  21. 13
  22. 38th
  23. 100
  24. 29
  25. 222
  26. 16
  27. 465
  28. 249
  29. 1225
  30. 16
  31. 35
  32. 191
  33. 103
  34. 45
  35. 91
  36. 211
  37. 16th
  38. 13
  39. 36th
  40. 23rd

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