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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 182 · 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 8, 16, 24, ?, 40? (a) 33 (b) 32 (c) 40 (d) 31
  2. 2.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 210 (b) 228 (c) 420 (d) 34
  3. 3.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 99 (c) 29 (d) 198
  4. 4.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 253 (d) 506
  5. 5.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 45 (c) 90 (d) 10
  6. 6.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 110 (d) 19
  8. 8.What is the 11th term of the AP 20, 27, 34, 41, …? (a) 97 (b) 77 (c) 90 (d) 70
  9. 9.What is the 39th term of the AP 14, 21, 28, 35, …? (a) 280 (b) 266 (c) 273 (d) 287
  10. 10.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 504 (b) 32 (c) 264 (d) 252
  11. 11.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 400 (b) 200 (c) 38 (d) 220
  12. 12.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 10 (c) 60 (d) 55
  13. 13.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 17 (b) 19 (c) 18 (d) 22
  14. 14.Which term of the AP 12, 21, 30, 39, … is 138? (a) 17th (b) 15th (c) 14th (d) 16th
  15. 15.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 15 (b) 14 (c) 24 (d) 16
  16. 16.What is the 20th term of the AP 5, 12, 19, 26, …? (a) 138 (b) 145 (c) 133 (d) 140
  17. 17.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 204 (b) 408 (c) 216 (d) 28
  18. 18.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 4186 (d) 8372
  19. 19.What is the 33rd term of the AP 3, 5, 7, 9, …? (a) 64 (b) 67 (c) 69 (d) 66
  20. 20.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 496 (d) 1056
  21. 21.What is the 23rd term of the AP 14, 22, 30, 38, …? (a) 198 (b) 176 (c) 184 (d) 190
  22. 22.What is the missing term in the AP 12, 16, 20, ?, 28? (a) 28 (b) 24 (c) 25 (d) 23
  23. 23.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 12 (b) 13 (c) 19 (d) 14
  24. 24.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 27 (d) 210
  25. 25.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2279 (c) 2211 (d) 2278
  26. 26.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  27. 27.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 650 (d) 325
  28. 28.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 216 (b) 20 (c) 108 (d) 117
  29. 29.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 13 (b) 12 (c) 11 (d) 10
  30. 30.What is the 27th term of the AP 14, 19, 24, 29, …? (a) 149 (b) 144 (c) 135 (d) 130
  31. 31.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 16 (b) 17 (c) 15 (d) 21
  32. 32.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
  33. 33.What is the 24th term of the AP 15, 19, 23, 27, …? (a) 92 (b) 111 (c) 96 (d) 107
  34. 34.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 45 (c) 110 (d) 50
  35. 35.Which term of the AP 3, 6, 9, 12, … is 42? (a) 13th (b) 16th (c) 14th (d) 15th
  36. 36.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 176 (b) 13 (c) 88 (d) 89
  37. 37.What is the sum of all the whole numbers from 1 to 75? (a) 5700 (b) 2851 (c) 2850 (d) 2775
  38. 38.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 13 (b) 16 (c) 12 (d) 14
  39. 39.What is the 13th term of the AP 16, 23, 30, 37, …? (a) 100 (b) 91 (c) 107 (d) 84
  40. 40.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 90 (b) 180 (c) 96 (d) 13

Answer key

  1. 32
  2. 210
  3. 99
  4. 484
  5. 45
  6. 91
  7. 100
  8. 90
  9. 280
  10. 252
  11. 200
  12. 55
  13. 18
  14. 15th
  15. 15
  16. 138
  17. 204
  18. 4186
  19. 67
  20. 528
  21. 190
  22. 24
  23. 13
  24. 196
  25. 2278
  26. 625
  27. 325
  28. 108
  29. 11
  30. 144
  31. 16
  32. 64
  33. 107
  34. 55
  35. 14th
  36. 88
  37. 2850
  38. 13
  39. 100
  40. 90

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