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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 337 · 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 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  2. 2.What is the 34th term of the AP 18, 24, 30, 36, …? (a) 216 (b) 222 (c) 198 (d) 204
  3. 3.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 182 (d) 91
  4. 4.What is the 12th term of the AP 2, 4, 6, 8, …? (a) 22 (b) 25 (c) 26 (d) 24
  5. 5.Which term of the AP 4, 11, 18, 25, … is 60? (a) 8th (b) 9th (c) 11th (d) 10th
  6. 6.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 12 (b) 11 (c) 14 (d) 10
  7. 7.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3081 (d) 3042
  8. 8.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 18 (b) 17 (c) 22 (d) 19
  9. 9.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 322 (b) 161 (c) 166 (d) 38
  10. 10.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 17 (b) 16 (c) 14 (d) 15
  11. 11.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 126 (b) 144 (c) 36 (d) 252
  12. 12.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 1640 (c) 820 (d) 800
  13. 13.Which term of the AP 20, 29, 38, 47, … is 344? (a) 39th (b) 36th (c) 37th (d) 38th
  14. 14.Which term of the AP 5, 14, 23, 32, … is 149? (a) 17th (b) 19th (c) 18th (d) 16th
  15. 15.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 51 (c) 50 (d) 12
  16. 16.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 732 (b) 366 (c) 396 (d) 58
  17. 17.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 370 (c) 61 (d) 340
  18. 18.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 22 (b) 18 (c) 17 (d) 19
  19. 19.What is the 15th term of the AP 1, 7, 13, 19, …? (a) 90 (b) 84 (c) 85 (d) 91
  20. 20.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  21. 21.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 270 (b) 27 (c) 138 (d) 135
  22. 22.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 17 (b) 22 (c) 18 (d) 19
  23. 23.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 78 (c) 77 (d) 12
  24. 24.What is the 39th term of the AP 9, 12, 15, 18, …? (a) 123 (b) 117 (c) 114 (d) 126
  25. 25.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3570 (c) 3486 (d) 7140
  26. 26.What is the 16th term of the AP 16, 22, 28, 34, …? (a) 112 (b) 90 (c) 96 (d) 106
  27. 27.What is the 20th term of the AP 1, 7, 13, 19, …? (a) 121 (b) 115 (c) 120 (d) 114
  28. 28.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 13 (b) 10 (c) 12 (d) 11
  29. 29.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 110 (b) 220 (c) 34 (d) 125
  30. 30.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 22 (b) 21 (c) 29 (d) 20
  31. 31.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 1953 (c) 1922 (d) 3906
  32. 32.What is the 40th term of the AP 20, 22, 24, 26, …? (a) 100 (b) 98 (c) 80 (d) 78
  33. 33.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 180 (c) 90 (d) 91
  34. 34.What is the 27th term of the AP 20, 24, 28, 32, …? (a) 104 (b) 124 (c) 108 (d) 128
  35. 35.What is the 15th term of the AP 12, 19, 26, 33, …? (a) 117 (b) 105 (c) 110 (d) 98
  36. 36.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 43 (b) 34 (c) 33 (d) 35
  37. 37.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 756 (c) 378 (d) 379
  38. 38.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 15 (d) 64
  39. 39.Which term of the AP 14, 23, 32, 41, … is 86? (a) 9th (b) 8th (c) 10th (d) 11th
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 42 (d) 11

Answer key

  1. 576
  2. 216
  3. 169
  4. 24
  5. 9th
  6. 11
  7. 3081
  8. 18
  9. 161
  10. 15
  11. 126
  12. 820
  13. 37th
  14. 17th
  15. 50
  16. 366
  17. 340
  18. 18
  19. 85
  20. 100
  21. 135
  22. 18
  23. 77
  24. 123
  25. 3570
  26. 106
  27. 115
  28. 11
  29. 110
  30. 21
  31. 1953
  32. 98
  33. 90
  34. 124
  35. 110
  36. 34
  37. 378
  38. 64
  39. 9th
  40. 36

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