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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 650 · 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 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  2. 2.Which term of the AP 18, 27, 36, 45, … is 189? (a) 19th (b) 21st (c) 22nd (d) 20th
  3. 3.What is the 18th term of the AP 19, 25, 31, 37, …? (a) 102 (b) 121 (c) 108 (d) 127
  4. 4.What is the 27th term of the AP 11, 14, 17, 20, …? (a) 81 (b) 89 (c) 92 (d) 78
  5. 5.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1250 (c) 1275 (d) 1225
  6. 6.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 40 (b) 32 (c) 31 (d) 30
  7. 7.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  8. 8.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 19 (c) 65 (d) 68
  9. 9.Which term of the AP 3, 5, 7, 9, … is 27? (a) 15th (b) 13th (c) 14th (d) 12th
  10. 10.Which term of the AP 18, 22, 26, 30, … is 98? (a) 23rd (b) 20th (c) 22nd (d) 21st
  11. 11.Which term of the AP 16, 20, 24, 28, … is 84? (a) 19th (b) 17th (c) 18th (d) 21st
  12. 12.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 30 (b) 31 (c) 8 (d) 60
  13. 13.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 93 (c) 28 (d) 108
  14. 14.Which term of the AP 7, 12, 17, 22, … is 77? (a) 17th (b) 16th (c) 14th (d) 15th
  15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  16. 16.Which term of the AP 15, 18, 21, 24, … is 108? (a) 36th (b) 33rd (c) 32nd (d) 31st
  17. 17.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 912 (b) 456 (c) 71 (d) 492
  18. 18.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 784 (d) 406
  19. 19.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2211 (c) 2145 (d) 2178
  20. 20.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 576 (b) 315 (c) 56 (d) 288
  21. 21.What is the 33rd term of the AP 6, 8, 10, 12, …? (a) 72 (b) 66 (c) 64 (d) 70
  22. 22.What is the 10th term of the AP 4, 6, 8, 10, …? (a) 18 (b) 20 (c) 22 (d) 24
  23. 23.What is the 30th term of the AP 3, 11, 19, 27, …? (a) 243 (b) 232 (c) 235 (d) 240
  24. 24.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2888 (c) 2926 (d) 5852
  25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 42 (d) 36
  26. 26.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 21 (b) 17 (c) 16 (d) 15
  27. 27.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 19 (b) 98 (c) 182 (d) 91
  28. 28.What is the 18th term of the AP 16, 18, 20, 22, …? (a) 50 (b) 36 (c) 34 (d) 52
  29. 29.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 4186 (c) 8556 (d) 4232
  30. 30.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 176 (b) 96 (c) 18 (d) 88
  31. 31.What is the missing term in the AP 12, 17, ?, 27, 32? (a) 23 (b) 27 (c) 21 (d) 22
  32. 32.What is the 15th term of the AP 3, 5, 7, 9, …? (a) 30 (b) 31 (c) 33 (d) 28
  33. 33.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 234 (b) 36 (c) 252 (d) 468
  34. 34.Which term of the AP 4, 7, 10, 13, … is 121? (a) 40th (b) 41st (c) 42nd (d) 39th
  35. 35.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 240 (b) 21 (c) 120 (d) 130
  36. 36.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 228 (b) 120 (c) 15 (d) 114
  37. 37.Which term of the AP 20, 29, 38, 47, … is 290? (a) 33rd (b) 31st (c) 30th (d) 32nd
  38. 38.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 32 (b) 34 (c) 38 (d) 33
  39. 39.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2556 (c) 2557 (d) 2485
  40. 40.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 14 (b) 16 (c) 12 (d) 13

Answer key

  1. 49
  2. 20th
  3. 121
  4. 89
  5. 1275
  6. 31
  7. 144
  8. 65
  9. 13th
  10. 21st
  11. 18th
  12. 30
  13. 93
  14. 15th
  15. 841
  16. 32nd
  17. 456
  18. 784
  19. 2211
  20. 288
  21. 70
  22. 22
  23. 235
  24. 2926
  25. 36
  26. 16
  27. 91
  28. 50
  29. 4278
  30. 88
  31. 22
  32. 31
  33. 234
  34. 40th
  35. 120
  36. 114
  37. 31st
  38. 33
  39. 2556
  40. 13

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