← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 903 · 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 35th term of the AP 3, 8, 13, 18, …? (a) 175 (b) 178 (c) 173 (d) 170
  2. 2.What is the 32nd term of the AP 4, 13, 22, 31, …? (a) 292 (b) 279 (c) 288 (d) 283
  3. 3.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 328 (b) 164 (c) 176 (d) 31
  4. 4.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 60 (c) 100 (d) 50
  5. 5.What is the sum of all the whole numbers from 1 to 79? (a) 6320 (b) 3081 (c) 3160 (d) 3161
  6. 6.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 13 (b) 9 (c) 8 (d) 10
  7. 7.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 435 (d) 870
  8. 8.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 280 (b) 23 (c) 150 (d) 140
  9. 9.What is the 23rd term of the AP 2, 7, 12, 17, …? (a) 117 (b) 115 (c) 112 (d) 110
  10. 10.What is the 25th term of the AP 3, 5, 7, 9, …? (a) 48 (b) 51 (c) 53 (d) 50
  11. 11.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 8 (b) 6 (c) 9 (d) 7
  12. 12.What is the 37th term of the AP 12, 14, 16, 18, …? (a) 86 (b) 84 (c) 72 (d) 74
  13. 13.Which term of the AP 10, 15, 20, 25, … is 75? (a) 16th (b) 13th (c) 15th (d) 14th
  14. 14.Which term of the AP 14, 23, 32, 41, … is 122? (a) 15th (b) 14th (c) 12th (d) 13th
  15. 15.Which term of the AP 15, 22, 29, 36, … is 197? (a) 27th (b) 28th (c) 29th (d) 26th
  16. 16.Which term of the AP 4, 12, 20, 28, … is 236? (a) 29th (b) 31st (c) 30th (d) 32nd
  17. 17.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 552 (c) 277 (d) 253
  18. 18.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4232 (c) 4278 (d) 4186
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  20. 20.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 128 (b) 72 (c) 64 (d) 15
  21. 21.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 91 (c) 182 (d) 92
  22. 22.Which term of the AP 1, 6, 11, 16, … is 86? (a) 17th (b) 20th (c) 18th (d) 19th
  23. 23.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 27 (b) 24 (c) 23 (d) 22
  24. 24.What is the 16th term of the AP 6, 11, 16, 21, …? (a) 81 (b) 86 (c) 80 (d) 75
  25. 25.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 4802 (c) 4753 (d) 9702
  26. 26.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 33 (b) 27 (c) 26 (d) 25
  27. 27.What is the 40th term of the AP 6, 9, 12, 15, …? (a) 126 (b) 117 (c) 120 (d) 123
  28. 28.What is the 18th term of the AP 10, 19, 28, 37, …? (a) 163 (b) 162 (c) 172 (d) 153
  29. 29.What is the 36th term of the AP 1, 5, 9, 13, …? (a) 145 (b) 144 (c) 140 (d) 141
  30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
  31. 31.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 35 (d) 70
  32. 32.What is the 12th term of the AP 18, 27, 36, 45, …? (a) 117 (b) 108 (c) 99 (d) 126
  33. 33.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 153 (c) 154 (d) 306
  34. 34.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 33 (d) 289
  35. 35.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 14 (b) 13 (c) 15 (d) 18
  36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 144 (d) 23
  37. 37.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1653 (d) 1711
  38. 38.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 170 (c) 180 (d) 340
  39. 39.What is the 31st term of the AP 3, 7, 11, 15, …? (a) 127 (b) 123 (c) 124 (d) 120
  40. 40.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3362 (c) 3321 (d) 3403

Answer key

  1. 173
  2. 283
  3. 164
  4. 50
  5. 3160
  6. 9
  7. 841
  8. 140
  9. 112
  10. 51
  11. 7
  12. 84
  13. 14th
  14. 13th
  15. 27th
  16. 30th
  17. 276
  18. 4278
  19. 25
  20. 64
  21. 91
  22. 18th
  23. 23
  24. 81
  25. 4851
  26. 26
  27. 123
  28. 163
  29. 141
  30. 64
  31. 35
  32. 117
  33. 153
  34. 289
  35. 14
  36. 144
  37. 1711
  38. 170
  39. 123
  40. 3403

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad