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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 178 · 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 32? (a) 528 (b) 496 (c) 1056 (d) 512
  2. 2.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 15 (b) 18 (c) 16 (d) 14
  3. 3.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 170 (b) 85 (c) 27 (d) 90
  4. 4.What is the 13th term of the AP 2, 7, 12, 17, …? (a) 67 (b) 60 (c) 65 (d) 62
  5. 5.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 34 (b) 26 (c) 28 (d) 27
  6. 6.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 13 (b) 18 (c) 14 (d) 12
  7. 7.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3655 (c) 3570 (d) 3656
  8. 8.What is the 28th term of the AP 4, 7, 10, 13, …? (a) 81 (b) 84 (c) 88 (d) 85
  9. 9.What is the 14th term of the AP 14, 20, 26, 32, …? (a) 98 (b) 92 (c) 78 (d) 84
  10. 10.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 39 (d) 420
  11. 11.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 10 (b) 13 (c) 12 (d) 11
  12. 12.What is the 30th term of the AP 10, 13, 16, 19, …? (a) 100 (b) 90 (c) 97 (d) 87
  13. 13.What is the 12th term of the AP 2, 5, 8, 11, …? (a) 38 (b) 33 (c) 35 (d) 36
  14. 14.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 156 (c) 66 (d) 78
  15. 15.What is the missing term in the AP 20, 25, 30, ?, 40? (a) 34 (b) 36 (c) 35 (d) 40
  16. 16.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 342 (c) 372 (d) 56
  17. 17.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 47 (c) 300 (d) 600
  18. 18.What is the 39th term of the AP 4, 13, 22, 31, …? (a) 342 (b) 355 (c) 351 (d) 346
  19. 19.What is the 38th term of the AP 11, 19, 27, 35, …? (a) 307 (b) 304 (c) 315 (d) 296
  20. 20.What is the 38th term of the AP 15, 21, 27, 33, …? (a) 222 (b) 243 (c) 228 (d) 237
  21. 21.What is the 23rd term of the AP 10, 14, 18, 22, …? (a) 98 (b) 92 (c) 102 (d) 88
  22. 22.What is the 38th term of the AP 6, 12, 18, 24, …? (a) 222 (b) 229 (c) 228 (d) 234
  23. 23.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 17 (b) 11 (c) 10 (d) 9
  24. 24.Which term of the AP 20, 25, 30, 35, … is 90? (a) 14th (b) 15th (c) 18th (d) 16th
  25. 25.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 24 (b) 32 (c) 25 (d) 26
  26. 26.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 46 (b) 392 (c) 217 (d) 196
  27. 27.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 326 (c) 650 (d) 325
  28. 28.What is the sum of all the whole numbers from 1 to 70? (a) 4970 (b) 2450 (c) 2485 (d) 2415
  29. 29.Which term of the AP 14, 22, 30, 38, … is 214? (a) 25th (b) 26th (c) 27th (d) 28th
  30. 30.What is the 26th term of the AP 14, 21, 28, 35, …? (a) 196 (b) 189 (c) 175 (d) 182
  31. 31.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 77 (b) 154 (c) 80 (d) 20
  32. 32.Which term of the AP 11, 17, 23, 29, … is 185? (a) 29th (b) 30th (c) 32nd (d) 31st
  33. 33.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 266 (b) 154 (c) 133 (d) 37
  34. 34.Which term of the AP 5, 10, 15, 20, … is 115? (a) 22nd (b) 24th (c) 23rd (d) 25th
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  36. 36.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 31 (b) 41 (c) 32 (d) 33
  37. 37.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 28 (b) 27 (c) 26 (d) 33
  38. 38.What is the 39th term of the AP 6, 9, 12, 15, …? (a) 123 (b) 120 (c) 117 (d) 114
  39. 39.Which term of the AP 12, 21, 30, 39, … is 273? (a) 30th (b) 32nd (c) 31st (d) 29th
  40. 40.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 33 (c) 138 (d) 246

Answer key

  1. 528
  2. 15
  3. 85
  4. 62
  5. 27
  6. 13
  7. 3655
  8. 85
  9. 92
  10. 400
  11. 11
  12. 97
  13. 35
  14. 78
  15. 35
  16. 342
  17. 300
  18. 346
  19. 307
  20. 237
  21. 98
  22. 228
  23. 10
  24. 15th
  25. 25
  26. 196
  27. 325
  28. 2485
  29. 26th
  30. 189
  31. 77
  32. 30th
  33. 133
  34. 23rd
  35. 121
  36. 32
  37. 27
  38. 120
  39. 30th
  40. 123

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