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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 231 · 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 missing term in the AP 5, ?, 9, 11, 13? (a) 7 (b) 8 (c) 9 (d) 6
  2. 2.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 224 (b) 46 (c) 400 (d) 200
  3. 3.Which term of the AP 19, 28, 37, 46, … is 109? (a) 10th (b) 13th (c) 11th (d) 12th
  4. 4.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 1122 (c) 562 (d) 561
  5. 5.What is the missing term in the AP 4, 9, 14, ?, 24? (a) 18 (b) 20 (c) 24 (d) 19
  6. 6.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 145 (b) 160 (c) 28 (d) 290
  7. 7.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 660 (b) 55 (c) 335 (d) 330
  8. 8.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 15 (b) 99 (c) 198 (d) 100
  9. 9.What is the 29th term of the AP 2, 11, 20, 29, …? (a) 263 (b) 254 (c) 261 (d) 252
  10. 10.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 110 (b) 220 (c) 15 (d) 111
  11. 11.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2701 (c) 2628 (d) 2702
  12. 12.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2016 (c) 2017 (d) 4032
  13. 13.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 89 (b) 176 (c) 13 (d) 88
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
  15. 15.What is the 21st term of the AP 11, 19, 27, 35, …? (a) 179 (b) 168 (c) 160 (d) 171
  16. 16.What is the 38th term of the AP 13, 22, 31, 40, …? (a) 355 (b) 342 (c) 346 (d) 333
  17. 17.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 25 (c) 224 (d) 112
  18. 18.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 306 (c) 136 (d) 154
  19. 19.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 36 (c) 8 (d) 40
  20. 20.Which term of the AP 16, 21, 26, 31, … is 141? (a) 28th (b) 26th (c) 25th (d) 27th
  21. 21.What is the 14th term of the AP 3, 11, 19, 27, …? (a) 115 (b) 104 (c) 107 (d) 112
  22. 22.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 69 (c) 14 (d) 138
  23. 23.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 496 (c) 465 (d) 992
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 17 (d) 81
  25. 25.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 253 (d) 484
  26. 26.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 6 (b) 4 (c) 5 (d) 7
  27. 27.What is the 10th term of the AP 10, 19, 28, 37, …? (a) 91 (b) 90 (c) 81 (d) 100
  28. 28.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 55 (b) 110 (c) 58 (d) 17
  29. 29.What is the 21st term of the AP 1, 6, 11, 16, …? (a) 100 (b) 106 (c) 105 (d) 101
  30. 30.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 138 (b) 33 (c) 246 (d) 123
  31. 31.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  32. 32.What is the 15th term of the AP 14, 17, 20, 23, …? (a) 42 (b) 56 (c) 45 (d) 59
  33. 33.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 264 (c) 267 (d) 528
  34. 34.What is the 37th term of the AP 20, 22, 24, 26, …? (a) 72 (b) 92 (c) 94 (d) 74
  35. 35.Which term of the AP 7, 11, 15, 19, … is 51? (a) 11th (b) 13th (c) 12th (d) 14th
  36. 36.What is the 13th term of the AP 6, 13, 20, 27, …? (a) 84 (b) 90 (c) 97 (d) 91
  37. 37.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4371 (c) 4418 (d) 8930
  38. 38.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4656 (c) 9506 (d) 4754
  39. 39.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  40. 40.What is the 25th term of the AP 10, 19, 28, 37, …? (a) 216 (b) 226 (c) 225 (d) 235

Answer key

  1. 7
  2. 200
  3. 11th
  4. 561
  5. 19
  6. 145
  7. 330
  8. 99
  9. 254
  10. 110
  11. 2701
  12. 2016
  13. 88
  14. 576
  15. 171
  16. 346
  17. 112
  18. 153
  19. 36
  20. 26th
  21. 107
  22. 69
  23. 496
  24. 81
  25. 484
  26. 5
  27. 91
  28. 55
  29. 101
  30. 123
  31. 324
  32. 56
  33. 264
  34. 92
  35. 12th
  36. 90
  37. 4465
  38. 4753
  39. 2556
  40. 226

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