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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 651 · 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 all the whole numbers from 1 to 31? (a) 497 (b) 465 (c) 992 (d) 496
  2. 2.What is the 16th term of the AP 5, 14, 23, 32, …? (a) 149 (b) 144 (c) 135 (d) 140
  3. 3.What is the 34th term of the AP 20, 26, 32, 38, …? (a) 224 (b) 218 (c) 204 (d) 198
  4. 4.What is the 40th term of the AP 14, 19, 24, 29, …? (a) 200 (b) 195 (c) 209 (d) 214
  5. 5.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 27 (b) 25 (c) 23 (d) 24
  6. 6.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 5 (c) 16 (d) 15
  7. 7.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 8930 (c) 4418 (d) 4371
  8. 8.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 22 (b) 160 (c) 83 (d) 80
  9. 9.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 21 (b) 20 (c) 19 (d) 18
  10. 10.Which term of the AP 10, 12, 14, 16, … is 48? (a) 20th (b) 19th (c) 24th (d) 21st
  11. 11.What is the missing term in the AP 1, 9, ?, 25, 33? (a) 17 (b) 25 (c) 16 (d) 18
  12. 12.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 29 (b) 30 (c) 35 (d) 31
  13. 13.What is the 11th term of the AP 11, 13, 15, 17, …? (a) 22 (b) 31 (c) 20 (d) 33
  14. 14.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 198 (b) 201 (c) 396 (d) 34
  15. 15.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 210 (b) 24 (c) 108 (d) 105
  16. 16.Which term of the AP 19, 21, 23, 25, … is 59? (a) 20th (b) 22nd (c) 21st (d) 23rd
  17. 17.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 3782 (c) 1892 (d) 1830
  18. 18.What is the 28th term of the AP 10, 15, 20, 25, …? (a) 150 (b) 135 (c) 140 (d) 145
  19. 19.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 4032 (c) 1953 (d) 2017
  20. 20.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 264 (c) 132 (d) 133
  21. 21.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 732 (b) 58 (c) 396 (d) 366
  22. 22.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 432 (b) 48 (c) 216 (d) 240
  23. 23.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  24. 24.What is the 39th term of the AP 10, 13, 16, 19, …? (a) 127 (b) 114 (c) 117 (d) 124
  25. 25.What is the 33rd term of the AP 18, 26, 34, 42, …? (a) 256 (b) 274 (c) 264 (d) 282
  26. 26.What is the 13th term of the AP 20, 25, 30, 35, …? (a) 60 (b) 65 (c) 80 (d) 85
  27. 27.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 21 (b) 15 (c) 16 (d) 17
  28. 28.What is the 17th term of the AP 8, 14, 20, 26, …? (a) 110 (b) 96 (c) 104 (d) 102
  29. 29.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 240 (b) 30 (c) 132 (d) 120
  30. 30.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  31. 31.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4561 (c) 4465 (d) 4560
  32. 32.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 300 (c) 276 (d) 600
  33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  34. 34.What is the 32nd term of the AP 4, 9, 14, 19, …? (a) 160 (b) 155 (c) 164 (d) 159
  35. 35.What is the 24th term of the AP 6, 9, 12, 15, …? (a) 69 (b) 72 (c) 78 (d) 75
  36. 36.What is the 26th term of the AP 2, 6, 10, 14, …? (a) 106 (b) 102 (c) 104 (d) 100
  37. 37.What is the 19th term of the AP 9, 11, 13, 15, …? (a) 36 (b) 38 (c) 45 (d) 47
  38. 38.What is the 15th term of the AP 1, 4, 7, 10, …? (a) 46 (b) 42 (c) 43 (d) 45
  39. 39.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 196 (b) 112 (c) 26 (d) 98
  40. 40.Which term of the AP 11, 19, 27, 35, … is 259? (a) 34th (b) 31st (c) 32nd (d) 33rd

Answer key

  1. 496
  2. 140
  3. 218
  4. 209
  5. 24
  6. 15
  7. 4465
  8. 80
  9. 19
  10. 20th
  11. 17
  12. 30
  13. 31
  14. 198
  15. 105
  16. 21st
  17. 1891
  18. 145
  19. 2016
  20. 132
  21. 366
  22. 216
  23. 81
  24. 124
  25. 274
  26. 80
  27. 16
  28. 104
  29. 120
  30. 576
  31. 4560
  32. 300
  33. 400
  34. 159
  35. 75
  36. 102
  37. 45
  38. 43
  39. 98
  40. 32nd

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