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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 382 · 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.Which term of the AP 6, 13, 20, 27, … is 146? (a) 21st (b) 22nd (c) 23rd (d) 20th
  2. 2.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 15 (b) 63 (c) 126 (d) 70
  3. 3.Which term of the AP 4, 8, 12, 16, … is 96? (a) 25th (b) 26th (c) 24th (d) 23rd
  4. 4.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1568 (c) 3192 (d) 1596
  5. 5.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 2970 (c) 1458 (d) 1485
  6. 6.What is the 16th term of the AP 11, 13, 15, 17, …? (a) 30 (b) 43 (c) 41 (d) 32
  7. 7.Which term of the AP 20, 29, 38, 47, … is 92? (a) 9th (b) 10th (c) 11th (d) 8th
  8. 8.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 14 (b) 16 (c) 22 (d) 15
  9. 9.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 44 (b) 184 (c) 208 (d) 368
  10. 10.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 162 (c) 324 (d) 165
  11. 11.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 144 (b) 24 (c) 153 (d) 288
  12. 12.Which term of the AP 12, 17, 22, 27, … is 102? (a) 21st (b) 18th (c) 20th (d) 19th
  13. 13.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 351 (c) 378 (d) 379
  14. 14.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 180 (b) 165 (c) 330 (d) 30
  15. 15.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 60 (c) 108 (d) 54
  16. 16.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1596 (d) 1654
  17. 17.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 16 (b) 14 (c) 15 (d) 18
  18. 18.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 150 (b) 75 (c) 78 (d) 21
  19. 19.Which term of the AP 13, 16, 19, 22, … is 58? (a) 18th (b) 17th (c) 15th (d) 16th
  20. 20.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 363 (b) 63 (c) 726 (d) 396
  21. 21.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 595 (c) 1260 (d) 630
  22. 22.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 17 (b) 57 (c) 114 (d) 66
  23. 23.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 30 (c) 10 (d) 60
  24. 24.What is the 11th term of the AP 9, 16, 23, 30, …? (a) 86 (b) 70 (c) 79 (d) 77
  25. 25.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 81 (d) 90
  26. 26.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 66 (c) 72 (d) 156
  27. 27.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 101 (b) 196 (c) 23 (d) 98
  28. 28.Which term of the AP 16, 23, 30, 37, … is 177? (a) 23rd (b) 25th (c) 26th (d) 24th
  29. 29.What is the 37th term of the AP 9, 11, 13, 15, …? (a) 72 (b) 81 (c) 83 (d) 74
  30. 30.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 27 (d) 210
  31. 31.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 42 (b) 196 (c) 392 (d) 216
  32. 32.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 37 (b) 380 (c) 210 (d) 190
  33. 33.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4095 (c) 4187 (d) 4186
  34. 34.What is the 15th term of the AP 8, 11, 14, 17, …? (a) 42 (b) 53 (c) 45 (d) 50
  35. 35.What is the 22nd term of the AP 12, 14, 16, 18, …? (a) 44 (b) 56 (c) 42 (d) 54
  36. 36.Which term of the AP 13, 22, 31, 40, … is 355? (a) 38th (b) 40th (c) 39th (d) 41st
  37. 37.Which term of the AP 3, 9, 15, 21, … is 147? (a) 25th (b) 27th (c) 24th (d) 26th
  38. 38.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 17 (b) 118 (c) 117 (d) 234
  39. 39.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 190 (c) 110 (d) 95
  40. 40.What is the 37th term of the AP 11, 13, 15, 17, …? (a) 83 (b) 85 (c) 72 (d) 74

Answer key

  1. 21st
  2. 63
  3. 24th
  4. 1596
  5. 1485
  6. 41
  7. 9th
  8. 15
  9. 184
  10. 162
  11. 144
  12. 19th
  13. 378
  14. 165
  15. 54
  16. 1653
  17. 15
  18. 75
  19. 16th
  20. 363
  21. 630
  22. 57
  23. 30
  24. 79
  25. 81
  26. 78
  27. 98
  28. 24th
  29. 81
  30. 196
  31. 196
  32. 190
  33. 4186
  34. 50
  35. 54
  36. 39th
  37. 25th
  38. 117
  39. 95
  40. 83

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