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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 269 · 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 8, 13, 18, 23, … is 163? (a) 34th (b) 33rd (c) 32nd (d) 31st
  2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 78 (d) 23
  3. 3.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 91 (c) 78 (d) 182
  4. 4.What is the 36th term of the AP 5, 13, 21, 29, …? (a) 288 (b) 293 (c) 280 (d) 285
  5. 5.Which term of the AP 9, 17, 25, 33, … is 265? (a) 34th (b) 32nd (c) 33rd (d) 35th
  6. 6.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 144 (b) 256 (c) 30 (d) 128
  7. 7.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 43 (d) 253
  8. 8.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 42 (c) 24 (d) 21
  9. 9.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 84 (b) 168 (c) 96 (d) 24
  10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  11. 11.What is the 30th term of the AP 17, 22, 27, 32, …? (a) 162 (b) 167 (c) 145 (d) 150
  12. 12.What is the 18th term of the AP 4, 7, 10, 13, …? (a) 51 (b) 55 (c) 58 (d) 54
  13. 13.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 117 (b) 32 (c) 234 (d) 132
  14. 14.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 96 (b) 48 (c) 13 (d) 54
  15. 15.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 756 (d) 53
  17. 17.What is the 30th term of the AP 12, 20, 28, 36, …? (a) 232 (b) 244 (c) 240 (d) 252
  18. 18.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 21 (b) 20 (c) 25 (d) 22
  19. 19.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 75 (b) 12 (c) 150 (d) 80
  20. 20.What is the 17th term of the AP 15, 24, 33, 42, …? (a) 168 (b) 153 (c) 144 (d) 159
  21. 21.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2701 (c) 5402 (d) 2702
  22. 22.What is the 11th term of the AP 14, 16, 18, 20, …? (a) 36 (b) 20 (c) 34 (d) 22
  23. 23.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 5050 (c) 4950 (d) 10100
  24. 24.What is the 39th term of the AP 17, 23, 29, 35, …? (a) 234 (b) 245 (c) 251 (d) 228
  25. 25.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 21 (b) 90 (c) 81 (d) 162
  26. 26.What is the 26th term of the AP 9, 13, 17, 21, …? (a) 104 (b) 113 (c) 100 (d) 109
  27. 27.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 3161 (c) 3160 (d) 6320
  28. 28.What is the 14th term of the AP 16, 19, 22, 25, …? (a) 58 (b) 39 (c) 42 (d) 55
  29. 29.What is the 15th term of the AP 18, 27, 36, 45, …? (a) 126 (b) 144 (c) 153 (d) 135
  30. 30.What is the 10th term of the AP 14, 17, 20, 23, …? (a) 30 (b) 27 (c) 41 (d) 44
  31. 31.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 36 (b) 37 (c) 46 (d) 38
  32. 32.What is the 25th term of the AP 8, 17, 26, 35, …? (a) 224 (b) 225 (c) 233 (d) 216
  33. 33.Which term of the AP 7, 15, 23, 31, … is 127? (a) 15th (b) 16th (c) 17th (d) 18th
  34. 34.Which term of the AP 10, 14, 18, 22, … is 38? (a) 8th (b) 9th (c) 7th (d) 10th
  35. 35.What is the 22nd term of the AP 1, 6, 11, 16, …? (a) 106 (b) 105 (c) 111 (d) 110
  36. 36.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 210 (b) 120 (c) 33 (d) 105
  37. 37.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 43 (b) 41 (c) 42 (d) 50
  38. 38.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 240 (b) 264 (c) 51 (d) 480
  39. 39.What is the 16th term of the AP 18, 20, 22, 24, …? (a) 48 (b) 32 (c) 50 (d) 30
  40. 40.Which term of the AP 15, 21, 27, 33, … is 63? (a) 10th (b) 8th (c) 9th (d) 11th

Answer key

  1. 32nd
  2. 144
  3. 91
  4. 285
  5. 33rd
  6. 128
  7. 484
  8. 21
  9. 84
  10. 25
  11. 162
  12. 55
  13. 117
  14. 48
  15. 361
  16. 729
  17. 244
  18. 21
  19. 75
  20. 159
  21. 2701
  22. 34
  23. 5050
  24. 245
  25. 81
  26. 109
  27. 3160
  28. 55
  29. 144
  30. 41
  31. 37
  32. 224
  33. 16th
  34. 8th
  35. 106
  36. 105
  37. 42
  38. 240
  39. 48
  40. 9th

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