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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 15 · 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 19, 24, 29, 34, … is 54? (a) 8th (b) 9th (c) 7th (d) 10th
  2. 2.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 17 (b) 18 (c) 21 (d) 19
  3. 3.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 210 (c) 230 (d) 39
  4. 4.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 25 (b) 23 (c) 28 (d) 24
  5. 5.What is the missing term in the AP 10, 17, ?, 31, 38? (a) 24 (b) 23 (c) 31 (d) 25
  6. 6.What is the 25th term of the AP 18, 24, 30, 36, …? (a) 144 (b) 162 (c) 168 (d) 150
  7. 7.What is the 13th term of the AP 11, 18, 25, 32, …? (a) 95 (b) 84 (c) 102 (d) 91
  8. 8.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 9 (b) 15 (c) 10 (d) 8
  9. 9.What is the 33rd term of the AP 7, 13, 19, 25, …? (a) 198 (b) 199 (c) 192 (d) 205
  10. 10.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 150 (b) 75 (c) 78 (d) 21
  11. 11.What is the 26th term of the AP 20, 22, 24, 26, …? (a) 70 (b) 52 (c) 72 (d) 50
  12. 12.What is the 16th term of the AP 14, 22, 30, 38, …? (a) 142 (b) 128 (c) 134 (d) 120
  13. 13.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 150 (b) 156 (c) 300 (d) 18
  14. 14.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 232 (b) 416 (c) 208 (d) 47
  15. 15.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 12 (b) 14 (c) 20 (d) 13
  16. 16.What is the 10th term of the AP 12, 15, 18, 21, …? (a) 30 (b) 27 (c) 42 (d) 39
  17. 17.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 21 (c) 186 (d) 192
  18. 18.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 25 (b) 102 (c) 180 (d) 90
  19. 19.Which term of the AP 10, 16, 22, 28, … is 94? (a) 15th (b) 17th (c) 14th (d) 16th
  20. 20.What is the 31st term of the AP 6, 10, 14, 18, …? (a) 130 (b) 124 (c) 120 (d) 126
  21. 21.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 128 (b) 120 (c) 22 (d) 240
  22. 22.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 210 (d) 27
  23. 23.What is the 22nd term of the AP 6, 12, 18, 24, …? (a) 132 (b) 138 (c) 133 (d) 126
  24. 24.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 102 (c) 120 (d) 204
  25. 25.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 20 (b) 26 (c) 18 (d) 19
  26. 26.What is the 39th term of the AP 15, 22, 29, 36, …? (a) 273 (b) 266 (c) 281 (d) 288
  27. 27.What is the 37th term of the AP 11, 19, 27, 35, …? (a) 296 (b) 299 (c) 288 (d) 307
  28. 28.Which term of the AP 14, 16, 18, 20, … is 68? (a) 29th (b) 34th (c) 27th (d) 28th
  29. 29.What is the 16th term of the AP 1, 3, 5, 7, …? (a) 30 (b) 31 (c) 33 (d) 32
  30. 30.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 9 (d) 30
  31. 31.What is the 32nd term of the AP 6, 8, 10, 12, …? (a) 62 (b) 64 (c) 70 (d) 68
  32. 32.Which term of the AP 13, 17, 21, 25, … is 45? (a) 11th (b) 9th (c) 10th (d) 8th
  33. 33.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 5700 (c) 2851 (d) 2850
  34. 34.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 30 (b) 25 (c) 26 (d) 24
  35. 35.What is the 28th term of the AP 6, 11, 16, 21, …? (a) 141 (b) 135 (c) 140 (d) 146
  36. 36.What is the 29th term of the AP 5, 12, 19, 26, …? (a) 208 (b) 201 (c) 196 (d) 203
  37. 37.Which term of the AP 6, 14, 22, 30, … is 214? (a) 26th (b) 29th (c) 27th (d) 28th
  38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  39. 39.Which term of the AP 20, 27, 34, 41, … is 69? (a) 9th (b) 7th (c) 10th (d) 8th
  40. 40.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729

Answer key

  1. 8th
  2. 18
  3. 210
  4. 24
  5. 24
  6. 162
  7. 95
  8. 9
  9. 199
  10. 75
  11. 70
  12. 134
  13. 150
  14. 208
  15. 13
  16. 39
  17. 186
  18. 90
  19. 15th
  20. 126
  21. 120
  22. 196
  23. 132
  24. 102
  25. 19
  26. 281
  27. 299
  28. 28th
  29. 31
  30. 25
  31. 68
  32. 9th
  33. 2850
  34. 25
  35. 141
  36. 201
  37. 27th
  38. 361
  39. 8th
  40. 729

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