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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 205 · 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 sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 62 (c) 385 (d) 704
  2. 2.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 16 (b) 77 (c) 140 (d) 70
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  4. 4.What is the 28th term of the AP 15, 18, 21, 24, …? (a) 96 (b) 99 (c) 84 (d) 81
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 13 (d) 28
  6. 6.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  7. 7.Which term of the AP 15, 23, 31, 39, … is 223? (a) 26th (b) 27th (c) 28th (d) 29th
  8. 8.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 200 (b) 40 (c) 360 (d) 180
  9. 9.Which term of the AP 11, 18, 25, 32, … is 256? (a) 35th (b) 36th (c) 37th (d) 38th
  10. 10.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 240 (b) 29 (c) 120 (d) 136
  11. 11.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
  12. 12.Which term of the AP 2, 4, 6, 8, … is 74? (a) 36th (b) 39th (c) 38th (d) 37th
  13. 13.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3322 (c) 3321 (d) 6642
  14. 14.Which term of the AP 19, 22, 25, 28, … is 100? (a) 29th (b) 27th (c) 30th (d) 28th
  15. 15.What is the missing term in the AP 7, 12, 17, ?, 27? (a) 21 (b) 22 (c) 27 (d) 23
  16. 16.Which term of the AP 3, 9, 15, 21, … is 189? (a) 32nd (b) 31st (c) 33rd (d) 34th
  17. 17.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21
  18. 18.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 171 (c) 162 (d) 342
  19. 19.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 120 (b) 66 (c) 60 (d) 15
  20. 20.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 18 (b) 15 (c) 16 (d) 14
  21. 21.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 9 (b) 84 (c) 42 (d) 43
  22. 22.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 44 (b) 528 (c) 264 (d) 286
  23. 23.Which term of the AP 3, 12, 21, 30, … is 354? (a) 42nd (b) 41st (c) 40th (d) 39th
  24. 24.Which term of the AP 5, 7, 9, 11, … is 37? (a) 19th (b) 18th (c) 17th (d) 16th
  25. 25.What is the 26th term of the AP 13, 20, 27, 34, …? (a) 195 (b) 175 (c) 182 (d) 188
  26. 26.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 34 (b) 33 (c) 43 (d) 35
  27. 27.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
  28. 28.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 1482 (c) 741 (d) 703
  29. 29.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 165 (b) 308 (c) 24 (d) 154
  30. 30.What is the 18th term of the AP 3, 10, 17, 24, …? (a) 119 (b) 129 (c) 126 (d) 122
  31. 31.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 84 (b) 104 (c) 88 (d) 100
  32. 32.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 31 (b) 38 (c) 32 (d) 30
  33. 33.What is the 27th term of the AP 1, 6, 11, 16, …? (a) 131 (b) 130 (c) 135 (d) 136
  34. 34.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 21 (b) 27 (c) 20 (d) 19
  35. 35.Which term of the AP 19, 27, 35, 43, … is 139? (a) 18th (b) 17th (c) 16th (d) 15th
  36. 36.What is the 23rd term of the AP 10, 12, 14, 16, …? (a) 44 (b) 56 (c) 54 (d) 46
  37. 37.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 20 (b) 17 (c) 15 (d) 16
  38. 38.What is the 28th term of the AP 10, 16, 22, 28, …? (a) 172 (b) 168 (c) 162 (d) 178
  39. 39.Which term of the AP 12, 16, 20, 24, … is 40? (a) 7th (b) 8th (c) 10th (d) 9th
  40. 40.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1326 (c) 1352 (d) 1378

Answer key

  1. 352
  2. 70
  3. 225
  4. 96
  5. 49
  6. 169
  7. 27th
  8. 180
  9. 36th
  10. 120
  11. 256
  12. 37th
  13. 3321
  14. 28th
  15. 22
  16. 32nd
  17. 36
  18. 171
  19. 60
  20. 15
  21. 42
  22. 264
  23. 40th
  24. 17th
  25. 188
  26. 34
  27. 196
  28. 741
  29. 154
  30. 122
  31. 100
  32. 31
  33. 131
  34. 20
  35. 16th
  36. 54
  37. 16
  38. 172
  39. 8th
  40. 1378

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