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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 616 · 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 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  2. 2.What is the 15th term of the AP 18, 21, 24, 27, …? (a) 42 (b) 63 (c) 60 (d) 45
  3. 3.What is the 20th term of the AP 3, 8, 13, 18, …? (a) 100 (b) 95 (c) 98 (d) 103
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  5. 5.What is the 38th term of the AP 12, 18, 24, 30, …? (a) 222 (b) 234 (c) 240 (d) 228
  6. 6.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 22 (b) 20 (c) 19 (d) 21
  7. 7.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 625 (d) 49
  8. 8.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  9. 9.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 9702 (c) 4753 (d) 4851
  10. 10.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 462 (c) 210 (d) 231
  11. 11.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 562 (c) 1122 (d) 528
  12. 12.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 66 (d) 156
  13. 13.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 14 (b) 12 (c) 13 (d) 19
  14. 14.Which term of the AP 1, 8, 15, 22, … is 141? (a) 21st (b) 23rd (c) 22nd (d) 20th
  15. 15.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 192 (b) 31 (c) 96 (d) 114
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 42 (d) 36
  17. 17.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
  18. 18.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 21 (b) 27 (c) 20 (d) 19
  19. 19.Which term of the AP 1, 3, 5, 7, … is 59? (a) 29th (b) 30th (c) 32nd (d) 31st
  20. 20.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 41 (b) 194 (c) 378 (d) 189
  21. 21.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 228 (b) 120 (c) 15 (d) 114
  22. 22.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 21 (b) 24 (c) 20 (d) 19
  23. 23.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 126 (b) 31 (c) 111 (d) 222
  24. 24.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 7 (b) 6 (c) 8 (d) 9
  25. 25.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 144 (b) 288 (c) 162 (d) 39
  26. 26.Which term of the AP 10, 19, 28, 37, … is 298? (a) 33rd (b) 32nd (c) 34th (d) 35th
  27. 27.Which term of the AP 1, 4, 7, 10, … is 25? (a) 10th (b) 11th (c) 8th (d) 9th
  28. 28.What is the 19th term of the AP 10, 15, 20, 25, …? (a) 90 (b) 105 (c) 95 (d) 100
  29. 29.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 13 (b) 12 (c) 15 (d) 14
  30. 30.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 196 (b) 217 (c) 392 (d) 46
  31. 31.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 10 (c) 11 (d) 16
  32. 32.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 27 (d) 210
  33. 33.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 7832 (d) 3916
  34. 34.What is the 14th term of the AP 20, 25, 30, 35, …? (a) 90 (b) 65 (c) 70 (d) 85
  35. 35.What is the 15th term of the AP 9, 17, 25, 33, …? (a) 129 (b) 120 (c) 112 (d) 121
  36. 36.What is the 26th term of the AP 3, 5, 7, 9, …? (a) 50 (b) 53 (c) 52 (d) 55
  37. 37.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 108 (c) 99 (d) 24
  38. 38.Which term of the AP 3, 5, 7, 9, … is 79? (a) 38th (b) 40th (c) 39th (d) 41st
  39. 39.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 30 (b) 240 (c) 132 (d) 120
  40. 40.What is the 39th term of the AP 5, 14, 23, 32, …? (a) 342 (b) 347 (c) 351 (d) 356

Answer key

  1. 25
  2. 60
  3. 98
  4. 784
  5. 234
  6. 20
  7. 625
  8. 841
  9. 4851
  10. 231
  11. 561
  12. 78
  13. 13
  14. 21st
  15. 96
  16. 36
  17. 484
  18. 20
  19. 30th
  20. 189
  21. 114
  22. 20
  23. 111
  24. 7
  25. 144
  26. 33rd
  27. 9th
  28. 100
  29. 13
  30. 196
  31. 11
  32. 196
  33. 3916
  34. 85
  35. 121
  36. 53
  37. 99
  38. 39th
  39. 120
  40. 347

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