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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 719 · 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 10th term of the AP 13, 15, 17, 19, …? (a) 31 (b) 20 (c) 18 (d) 33
  2. 2.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 39 (d) 420
  3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 45 (d) 17
  4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42
  5. 5.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 168 (c) 84 (d) 87
  6. 6.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 76 (b) 552 (c) 516 (d) 1032
  7. 7.Which term of the AP 16, 20, 24, 28, … is 96? (a) 24th (b) 22nd (c) 21st (d) 20th
  8. 8.What is the 17th term of the AP 9, 16, 23, 30, …? (a) 112 (b) 128 (c) 119 (d) 121
  9. 9.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 30 (b) 312 (c) 168 (d) 156
  10. 10.Which term of the AP 15, 20, 25, 30, … is 100? (a) 18th (b) 17th (c) 20th (d) 19th
  11. 11.What is the 19th term of the AP 2, 8, 14, 20, …? (a) 110 (b) 108 (c) 116 (d) 114
  12. 12.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 3741 (c) 3829 (d) 7656
  13. 13.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 32 (b) 119 (c) 124 (d) 238
  14. 14.What is the 22nd term of the AP 15, 24, 33, 42, …? (a) 213 (b) 198 (c) 204 (d) 189
  15. 15.Which term of the AP 17, 25, 33, 41, … is 81? (a) 9th (b) 11th (c) 10th (d) 8th
  16. 16.What is the 15th term of the AP 1, 3, 5, 7, …? (a) 28 (b) 30 (c) 29 (d) 31
  17. 17.What is the 23rd term of the AP 15, 24, 33, 42, …? (a) 213 (b) 222 (c) 207 (d) 198
  18. 18.What is the 20th term of the AP 19, 22, 25, 28, …? (a) 57 (b) 60 (c) 76 (d) 79
  19. 19.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 588 (b) 312 (c) 294 (d) 41
  20. 20.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 14 (b) 19 (c) 15 (d) 16
  21. 21.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 152 (b) 33 (c) 168 (d) 304
  22. 22.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 336 (b) 360 (c) 50 (d) 672
  23. 23.What is the 24th term of the AP 17, 20, 23, 26, …? (a) 72 (b) 86 (c) 69 (d) 89
  24. 24.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3570 (c) 7140 (d) 3486
  25. 25.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 37 (b) 154 (c) 159 (d) 308
  26. 26.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 23 (b) 28 (c) 21 (d) 22
  27. 27.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  28. 28.What is the 16th term of the AP 6, 11, 16, 21, …? (a) 81 (b) 80 (c) 75 (d) 86
  29. 29.What is the 34th term of the AP 13, 15, 17, 19, …? (a) 81 (b) 66 (c) 68 (d) 79
  30. 30.What is the 35th term of the AP 6, 12, 18, 24, …? (a) 204 (b) 210 (c) 216 (d) 211
  31. 31.Which term of the AP 19, 24, 29, 34, … is 54? (a) 9th (b) 10th (c) 7th (d) 8th
  32. 32.What is the 40th term of the AP 11, 16, 21, 26, …? (a) 211 (b) 200 (c) 195 (d) 206
  33. 33.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 26 (b) 25 (c) 24 (d) 32
  34. 34.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 50 (c) 100 (d) 60
  35. 35.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 55 (b) 56 (c) 110 (d) 13
  36. 36.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 1771 (c) 3540 (d) 1711
  37. 37.What is the missing term in the AP 5, ?, 21, 29, 37? (a) 14 (b) 12 (c) 13 (d) 21
  38. 38.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 20 (b) 22 (c) 21 (d) 27
  39. 39.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 145 (b) 290 (c) 19 (d) 150
  40. 40.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 26 (b) 25 (c) 27 (d) 33

Answer key

  1. 31
  2. 400
  3. 81
  4. 36
  5. 84
  6. 516
  7. 21st
  8. 121
  9. 156
  10. 18th
  11. 110
  12. 3828
  13. 119
  14. 204
  15. 9th
  16. 29
  17. 213
  18. 76
  19. 294
  20. 15
  21. 152
  22. 336
  23. 86
  24. 3570
  25. 154
  26. 22
  27. 441
  28. 81
  29. 79
  30. 210
  31. 8th
  32. 206
  33. 25
  34. 50
  35. 55
  36. 1770
  37. 13
  38. 21
  39. 145
  40. 26

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