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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 176 · 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 12 terms of the AP 4, 7, 10, …? (a) 264 (b) 37 (c) 492 (d) 246
  2. 2.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 124 (b) 119 (c) 238 (d) 32
  3. 3.Which term of the AP 9, 15, 21, 27, … is 93? (a) 15th (b) 14th (c) 16th (d) 17th
  4. 4.What is the 13th term of the AP 13, 22, 31, 40, …? (a) 121 (b) 130 (c) 108 (d) 117
  5. 5.What is the 26th term of the AP 1, 6, 11, 16, …? (a) 125 (b) 126 (c) 131 (d) 130
  6. 6.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4560 (c) 4656 (d) 4608
  7. 7.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 29 (d) 120
  8. 8.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 166 (b) 161 (c) 322 (d) 38
  9. 9.What is the 16th term of the AP 2, 9, 16, 23, …? (a) 114 (b) 105 (c) 112 (d) 107
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 529 (d) 276
  11. 11.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 25 (b) 80 (c) 150 (d) 75
  12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 17 (d) 45
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  14. 14.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
  15. 15.Which term of the AP 1, 4, 7, 10, … is 28? (a) 9th (b) 11th (c) 12th (d) 10th
  16. 16.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 150 (b) 40 (c) 300 (d) 168
  17. 17.What is the sum of the first 8 terms of the AP 6, 11, 16, …? (a) 41 (b) 376 (c) 208 (d) 188
  18. 18.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 12 (c) 45 (d) 40
  19. 19.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 190 (d) 200
  20. 20.What is the 11th term of the AP 9, 15, 21, 27, …? (a) 66 (b) 75 (c) 69 (d) 60
  21. 21.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 11 (b) 9 (c) 10 (d) 8
  22. 22.What is the 37th term of the AP 20, 22, 24, 26, …? (a) 74 (b) 94 (c) 72 (d) 92
  23. 23.What is the 14th term of the AP 17, 21, 25, 29, …? (a) 73 (b) 56 (c) 52 (d) 69
  24. 24.What is the 29th term of the AP 1, 3, 5, 7, …? (a) 59 (b) 58 (c) 56 (d) 57
  25. 25.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 272 (d) 31
  26. 26.What is the 24th term of the AP 11, 14, 17, 20, …? (a) 72 (b) 69 (c) 80 (d) 83
  27. 27.What is the 17th term of the AP 3, 11, 19, 27, …? (a) 131 (b) 136 (c) 139 (d) 128
  28. 28.What is the 26th term of the AP 4, 8, 12, 16, …? (a) 108 (b) 100 (c) 104 (d) 105
  29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 39 (d) 420
  30. 30.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 560 (b) 280 (c) 310 (d) 55
  31. 31.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 8 (b) 36 (c) 72 (d) 40
  32. 32.What is the 33rd term of the AP 11, 13, 15, 17, …? (a) 77 (b) 75 (c) 66 (d) 64
  33. 33.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 325 (d) 702
  34. 34.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 15 (b) 13 (c) 23 (d) 14
  35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  36. 36.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 78 (b) 75 (c) 150 (d) 21
  37. 37.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 182 (c) 91 (d) 92
  38. 38.What is the 18th term of the AP 18, 26, 34, 42, …? (a) 154 (b) 136 (c) 162 (d) 144
  39. 39.Which term of the AP 11, 15, 19, 23, … is 151? (a) 35th (b) 37th (c) 36th (d) 38th
  40. 40.What is the 34th term of the AP 20, 23, 26, 29, …? (a) 99 (b) 122 (c) 102 (d) 119

Answer key

  1. 246
  2. 119
  3. 15th
  4. 121
  5. 126
  6. 4656
  7. 225
  8. 161
  9. 107
  10. 529
  11. 75
  12. 81
  13. 676
  14. 361
  15. 10th
  16. 150
  17. 188
  18. 40
  19. 210
  20. 69
  21. 9
  22. 92
  23. 69
  24. 57
  25. 256
  26. 80
  27. 131
  28. 104
  29. 400
  30. 280
  31. 36
  32. 75
  33. 351
  34. 14
  35. 289
  36. 75
  37. 91
  38. 154
  39. 36th
  40. 119

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