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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 24 · 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 missing term in the AP 11, ?, 27, 35, 43? (a) 18 (b) 19 (c) 20 (d) 27
  2. 2.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 98 (c) 210 (d) 105
  3. 3.Which term of the AP 18, 26, 34, 42, … is 314? (a) 38th (b) 37th (c) 40th (d) 39th
  4. 4.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 984 (b) 528 (c) 74 (d) 492
  5. 5.What is the 28th term of the AP 1, 6, 11, 16, …? (a) 135 (b) 140 (c) 141 (d) 136
  6. 6.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 144 (b) 272 (c) 136 (d) 24
  7. 7.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 22 (b) 20 (c) 21 (d) 19
  8. 8.What is the 36th term of the AP 15, 20, 25, 30, …? (a) 190 (b) 175 (c) 195 (d) 180
  9. 9.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 54 (b) 108 (c) 14 (d) 60
  10. 10.What is the 11th term of the AP 7, 9, 11, 13, …? (a) 20 (b) 22 (c) 29 (d) 27
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 42 (d) 36
  12. 12.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 9 (b) 88 (c) 44 (d) 48
  13. 13.What is the 13th term of the AP 11, 17, 23, 29, …? (a) 83 (b) 72 (c) 89 (d) 78
  14. 14.Which term of the AP 9, 12, 15, 18, … is 75? (a) 22nd (b) 24th (c) 23rd (d) 25th
  15. 15.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 17 (c) 118 (d) 117
  16. 16.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 781 (c) 780 (d) 1560
  17. 17.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 252 (b) 264 (c) 504 (d) 32
  18. 18.What is the 23rd term of the AP 2, 8, 14, 20, …? (a) 134 (b) 132 (c) 140 (d) 138
  19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
  20. 20.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 32 (b) 25 (c) 26 (d) 27
  21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 210 (d) 196
  22. 22.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 24 (b) 90 (c) 80 (d) 160
  23. 23.What is the 17th term of the AP 11, 15, 19, 23, …? (a) 79 (b) 75 (c) 68 (d) 64
  24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 51 (c) 351 (d) 676
  25. 25.What is the 25th term of the AP 19, 27, 35, 43, …? (a) 219 (b) 200 (c) 192 (d) 211
  26. 26.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 47 (b) 37 (c) 39 (d) 38
  27. 27.Which term of the AP 2, 10, 18, 26, … is 138? (a) 19th (b) 20th (c) 17th (d) 18th
  28. 28.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 43 (b) 275 (c) 506 (d) 253
  29. 29.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 1640 (c) 820 (d) 780
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  31. 31.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4753 (c) 9506 (d) 4656
  32. 32.What is the 13th term of the AP 4, 13, 22, 31, …? (a) 112 (b) 108 (c) 117 (d) 121
  33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  34. 34.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 138 (b) 33 (c) 246 (d) 123
  35. 35.What is the 10th term of the AP 4, 7, 10, 13, …? (a) 27 (b) 31 (c) 34 (d) 30
  36. 36.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 6 (b) 12 (c) 8 (d) 7
  37. 37.What is the 35th term of the AP 7, 10, 13, 16, …? (a) 109 (b) 112 (c) 102 (d) 105
  38. 38.What is the 19th term of the AP 17, 24, 31, 38, …? (a) 126 (b) 133 (c) 150 (d) 143
  39. 39.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 42 (b) 189 (c) 336 (d) 168
  40. 40.What is the missing term in the AP 16, ?, 34, 43, 52? (a) 25 (b) 26 (c) 34 (d) 24

Answer key

  1. 19
  2. 105
  3. 38th
  4. 492
  5. 136
  6. 136
  7. 20
  8. 190
  9. 54
  10. 27
  11. 36
  12. 44
  13. 83
  14. 23rd
  15. 117
  16. 780
  17. 252
  18. 134
  19. 484
  20. 26
  21. 196
  22. 80
  23. 75
  24. 676
  25. 211
  26. 38
  27. 18th
  28. 253
  29. 820
  30. 144
  31. 4753
  32. 112
  33. 256
  34. 123
  35. 31
  36. 7
  37. 109
  38. 143
  39. 168
  40. 25

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