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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 25 · 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 12, ?, 20, 24, 28? (a) 16 (b) 20 (c) 17 (d) 15
  2. 2.What is the 20th term of the AP 19, 28, 37, 46, …? (a) 171 (b) 180 (c) 199 (d) 190
  3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 153 (d) 33
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  5. 5.What is the 25th term of the AP 9, 12, 15, 18, …? (a) 81 (b) 84 (c) 72 (d) 75
  6. 6.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 4 (b) 6 (c) 5 (d) 9
  7. 7.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 22 (b) 20 (c) 21 (d) 27
  8. 8.What is the 16th term of the AP 4, 9, 14, 19, …? (a) 75 (b) 80 (c) 84 (d) 79
  9. 9.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 5256 (c) 2628 (d) 2592
  10. 10.What is the 30th term of the AP 18, 23, 28, 33, …? (a) 168 (b) 145 (c) 163 (d) 150
  11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 90 (d) 17
  12. 12.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 52 (b) 720 (c) 360 (d) 384
  13. 13.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 7 (b) 6 (c) 11 (d) 5
  14. 14.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 650 (d) 300
  15. 15.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 140 (b) 126 (c) 30 (d) 252
  16. 16.What is the 10th term of the AP 5, 10, 15, 20, …? (a) 50 (b) 51 (c) 45 (d) 55
  17. 17.Which term of the AP 1, 4, 7, 10, … is 103? (a) 37th (b) 36th (c) 34th (d) 35th
  18. 18.What is the 36th term of the AP 19, 28, 37, 46, …? (a) 315 (b) 343 (c) 324 (d) 334
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
  20. 20.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 65 (b) 11 (c) 130 (d) 70
  21. 21.Which term of the AP 12, 14, 16, 18, … is 84? (a) 36th (b) 37th (c) 42nd (d) 38th
  22. 22.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 9 (b) 11 (c) 10 (d) 14
  23. 23.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 385 (b) 62 (c) 704 (d) 352
  24. 24.Which term of the AP 14, 22, 30, 38, … is 94? (a) 12th (b) 11th (c) 13th (d) 10th
  25. 25.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 54 (b) 13 (c) 48 (d) 96
  26. 26.What is the missing term in the AP 7, ?, 23, 31, 39? (a) 15 (b) 16 (c) 14 (d) 23
  27. 27.What is the missing term in the AP 14, 19, ?, 29, 34? (a) 23 (b) 24 (c) 29 (d) 25
  28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  29. 29.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2556 (c) 5112 (d) 2485
  30. 30.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 126 (b) 64 (c) 63 (d) 12
  31. 31.What is the 29th term of the AP 19, 23, 27, 31, …? (a) 112 (b) 135 (c) 116 (d) 131
  32. 32.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 45 (b) 240 (c) 220 (d) 440
  33. 33.What is the 33rd term of the AP 15, 22, 29, 36, …? (a) 239 (b) 231 (c) 224 (d) 246
  34. 34.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 194 (b) 41 (c) 378 (d) 189
  35. 35.What is the 31st term of the AP 5, 10, 15, 20, …? (a) 160 (b) 155 (c) 156 (d) 150
  36. 36.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 91 (d) 92
  37. 37.What is the 10th term of the AP 17, 21, 25, 29, …? (a) 36 (b) 40 (c) 57 (d) 53
  38. 38.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 162 (b) 324 (c) 34 (d) 180
  39. 39.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 16 (b) 66 (c) 72 (d) 132
  40. 40.Which term of the AP 8, 15, 22, 29, … is 148? (a) 22nd (b) 23rd (c) 20th (d) 21st

Answer key

  1. 16
  2. 190
  3. 289
  4. 900
  5. 81
  6. 5
  7. 21
  8. 79
  9. 2628
  10. 163
  11. 81
  12. 360
  13. 6
  14. 325
  15. 126
  16. 50
  17. 35th
  18. 334
  19. 64
  20. 65
  21. 37th
  22. 10
  23. 352
  24. 11th
  25. 48
  26. 15
  27. 24
  28. 25
  29. 2556
  30. 63
  31. 131
  32. 220
  33. 239
  34. 189
  35. 155
  36. 91
  37. 53
  38. 162
  39. 66
  40. 21st

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