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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 617 · 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 5 terms of the AP 8, 9, 10, …? (a) 12 (b) 50 (c) 51 (d) 100
  2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 21 (d) 66
  3. 3.What is the 20th term of the AP 10, 17, 24, 31, …? (a) 143 (b) 150 (c) 133 (d) 140
  4. 4.What is the 12th term of the AP 3, 6, 9, 12, …? (a) 39 (b) 37 (c) 36 (d) 33
  5. 5.Which term of the AP 19, 26, 33, 40, … is 166? (a) 24th (b) 23rd (c) 22nd (d) 21st
  6. 6.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 1226 (c) 2450 (d) 1176
  7. 7.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 7656 (c) 3828 (d) 3829
  8. 8.What is the 34th term of the AP 17, 20, 23, 26, …? (a) 102 (b) 99 (c) 119 (d) 116
  9. 9.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 77 (b) 154 (c) 84 (d) 17
  10. 10.Which term of the AP 3, 11, 19, 27, … is 275? (a) 34th (b) 37th (c) 35th (d) 36th
  11. 11.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 204 (b) 27 (c) 384 (d) 192
  12. 12.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 156 (b) 150 (c) 300 (d) 18
  13. 13.What is the 24th term of the AP 17, 19, 21, 23, …? (a) 46 (b) 65 (c) 63 (d) 48
  14. 14.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 24 (b) 25 (c) 23 (d) 31
  15. 15.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 17 (b) 16 (c) 15 (d) 19
  16. 16.What is the 33rd term of the AP 11, 20, 29, 38, …? (a) 297 (b) 288 (c) 299 (d) 308
  17. 17.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 230 (b) 210 (c) 39 (d) 420
  18. 18.Which term of the AP 12, 14, 16, 18, … is 32? (a) 12th (b) 11th (c) 10th (d) 16th
  19. 19.Which term of the AP 9, 16, 23, 30, … is 254? (a) 35th (b) 38th (c) 37th (d) 36th
  20. 20.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 516 (b) 552 (c) 76 (d) 1032
  21. 21.What is the 26th term of the AP 17, 25, 33, 41, …? (a) 208 (b) 217 (c) 225 (d) 200
  22. 22.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 804 (b) 61 (c) 432 (d) 402
  23. 23.Which term of the AP 16, 22, 28, 34, … is 214? (a) 33rd (b) 36th (c) 34th (d) 35th
  24. 24.What is the 24th term of the AP 4, 6, 8, 10, …? (a) 46 (b) 48 (c) 50 (d) 52
  25. 25.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 45 (b) 17 (c) 55 (d) 90
  26. 26.What is the 14th term of the AP 13, 21, 29, 37, …? (a) 125 (b) 112 (c) 117 (d) 104
  27. 27.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 22 (b) 104 (c) 92 (d) 184
  28. 28.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4465 (c) 4561 (d) 4560
  29. 29.What is the 17th term of the AP 17, 21, 25, 29, …? (a) 68 (b) 85 (c) 81 (d) 64
  30. 30.What is the 32nd term of the AP 7, 16, 25, 34, …? (a) 286 (b) 295 (c) 279 (d) 288
  31. 31.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 624 (b) 312 (c) 336 (d) 48
  32. 32.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
  33. 33.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 33 (b) 27 (c) 28 (d) 29
  34. 34.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 34 (b) 30 (c) 29 (d) 31
  35. 35.Which term of the AP 8, 12, 16, 20, … is 84? (a) 21st (b) 19th (c) 20th (d) 22nd
  36. 36.What is the 33rd term of the AP 18, 21, 24, 27, …? (a) 96 (b) 117 (c) 114 (d) 99
  37. 37.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 38 (c) 506 (d) 253
  38. 38.What is the 16th term of the AP 4, 9, 14, 19, …? (a) 84 (b) 75 (c) 79 (d) 80
  39. 39.What is the 27th term of the AP 10, 12, 14, 16, …? (a) 64 (b) 54 (c) 52 (d) 62
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100

Answer key

  1. 50
  2. 121
  3. 143
  4. 36
  5. 22nd
  6. 1225
  7. 3828
  8. 116
  9. 77
  10. 35th
  11. 192
  12. 150
  13. 63
  14. 24
  15. 16
  16. 299
  17. 210
  18. 11th
  19. 36th
  20. 516
  21. 217
  22. 402
  23. 34th
  24. 50
  25. 45
  26. 117
  27. 92
  28. 4560
  29. 81
  30. 286
  31. 312
  32. 169
  33. 28
  34. 30
  35. 20th
  36. 114
  37. 253
  38. 79
  39. 62
  40. 100

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