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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 175 · 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.Which term of the AP 2, 4, 6, 8, … is 80? (a) 41st (b) 42nd (c) 40th (d) 39th
  2. 2.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4802 (c) 4851 (d) 4753
  3. 3.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 294 (b) 147 (c) 152 (d) 36
  4. 4.What is the 30th term of the AP 19, 24, 29, 34, …? (a) 169 (b) 145 (c) 164 (d) 150
  5. 5.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 16 (b) 18 (c) 14 (d) 15
  6. 6.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 122 (b) 26 (c) 119 (d) 238
  7. 7.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 13 (b) 180 (c) 96 (d) 90
  8. 8.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 8 (c) 35 (d) 70
  9. 9.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 22 (b) 20 (c) 21 (d) 24
  10. 10.Which term of the AP 9, 11, 13, 15, … is 57? (a) 25th (b) 27th (c) 24th (d) 26th
  11. 11.What is the 39th term of the AP 12, 19, 26, 33, …? (a) 266 (b) 278 (c) 273 (d) 285
  12. 12.What is the 38th term of the AP 1, 5, 9, 13, …? (a) 153 (b) 152 (c) 149 (d) 148
  13. 13.Which term of the AP 13, 18, 23, 28, … is 193? (a) 38th (b) 36th (c) 39th (d) 37th
  14. 14.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 297 (c) 319 (d) 47
  15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  16. 16.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  18. 18.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 90 (b) 46 (c) 45 (d) 9
  19. 19.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 6642 (c) 3240 (d) 3322
  20. 20.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 35 (b) 171 (c) 342 (d) 189
  21. 21.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 13 (b) 18 (c) 11 (d) 12
  22. 22.Which term of the AP 8, 10, 12, 14, … is 68? (a) 30th (b) 32nd (c) 31st (d) 34th
  23. 23.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 90 (c) 180 (d) 20
  24. 24.What is the 26th term of the AP 18, 25, 32, 39, …? (a) 182 (b) 200 (c) 193 (d) 175
  25. 25.What is the 28th term of the AP 3, 5, 7, 9, …? (a) 56 (b) 59 (c) 57 (d) 54
  26. 26.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  27. 27.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 29 (b) 240 (c) 120 (d) 136
  28. 28.What is the 18th term of the AP 8, 10, 12, 14, …? (a) 44 (b) 34 (c) 42 (d) 36
  29. 29.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 36 (b) 450 (c) 225 (d) 240
  30. 30.What is the 21st term of the AP 4, 8, 12, 16, …? (a) 85 (b) 80 (c) 88 (d) 84
  31. 31.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 120 (c) 240 (d) 121
  32. 32.Which term of the AP 16, 19, 22, 25, … is 55? (a) 13th (b) 15th (c) 14th (d) 16th
  33. 33.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 31 (b) 30 (c) 29 (d) 37
  34. 34.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 23 (b) 24 (c) 28 (d) 22
  35. 35.Which term of the AP 2, 6, 10, 14, … is 42? (a) 10th (b) 13th (c) 11th (d) 12th
  36. 36.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 351 (d) 51
  37. 37.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 5000 (d) 10100
  38. 38.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 30 (b) 32 (c) 38 (d) 31
  39. 39.What is the 23rd term of the AP 2, 8, 14, 20, …? (a) 140 (b) 138 (c) 134 (d) 132
  40. 40.What is the 21st term of the AP 2, 11, 20, 29, …? (a) 180 (b) 182 (c) 189 (d) 191

Answer key

  1. 40th
  2. 4851
  3. 147
  4. 164
  5. 15
  6. 119
  7. 90
  8. 35
  9. 21
  10. 25th
  11. 278
  12. 149
  13. 37th
  14. 297
  15. 36
  16. 144
  17. 100
  18. 45
  19. 3321
  20. 171
  21. 12
  22. 31st
  23. 90
  24. 193
  25. 57
  26. 441
  27. 120
  28. 42
  29. 225
  30. 84
  31. 120
  32. 14th
  33. 30
  34. 23
  35. 11th
  36. 676
  37. 5050
  38. 31
  39. 134
  40. 182

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