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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 598 · 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 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 9 (c) 36 (d) 35
  2. 2.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  3. 3.What is the 15th term of the AP 19, 23, 27, 31, …? (a) 79 (b) 60 (c) 75 (d) 56
  4. 4.Which term of the AP 14, 18, 22, 26, … is 118? (a) 29th (b) 27th (c) 26th (d) 28th
  5. 5.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 1653 (c) 1711 (d) 3422
  6. 6.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 8742 (c) 4371 (d) 4372
  7. 7.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 182 (d) 169
  8. 8.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 120 (c) 64 (d) 60
  9. 9.What is the missing term in the AP 12, ?, 16, 18, 20? (a) 16 (b) 15 (c) 13 (d) 14
  10. 10.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 729 (d) 756
  11. 11.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 60 (b) 21 (c) 110 (d) 55
  12. 12.What is the 18th term of the AP 8, 16, 24, 32, …? (a) 152 (b) 136 (c) 145 (d) 144
  13. 13.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 768 (b) 384 (c) 54 (d) 408
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 900 (d) 930
  15. 15.What is the 35th term of the AP 12, 19, 26, 33, …? (a) 245 (b) 238 (c) 250 (d) 257
  16. 16.What is the 29th term of the AP 19, 27, 35, 43, …? (a) 251 (b) 232 (c) 243 (d) 224
  17. 17.Which term of the AP 3, 7, 11, 15, … is 63? (a) 18th (b) 16th (c) 15th (d) 17th
  18. 18.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 32 (b) 119 (c) 238 (d) 124
  19. 19.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 351 (c) 325 (d) 338
  20. 20.What is the 38th term of the AP 4, 6, 8, 10, …? (a) 76 (b) 80 (c) 74 (d) 78
  21. 21.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 120 (c) 272 (d) 136
  22. 22.Which term of the AP 15, 23, 31, 39, … is 79? (a) 10th (b) 9th (c) 11th (d) 8th
  23. 23.Which term of the AP 12, 21, 30, 39, … is 291? (a) 33rd (b) 31st (c) 32nd (d) 34th
  24. 24.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 98 (b) 196 (c) 112 (d) 26
  25. 25.Which term of the AP 6, 10, 14, 18, … is 154? (a) 37th (b) 40th (c) 38th (d) 39th
  26. 26.What is the missing term in the AP 19, 26, 33, ?, 47? (a) 40 (b) 39 (c) 47 (d) 41
  27. 27.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  28. 28.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 35 (b) 34 (c) 44 (d) 36
  29. 29.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 72 (b) 468 (c) 504 (d) 936
  30. 30.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  31. 31.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 225 (c) 240 (d) 29
  32. 32.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 516 (b) 480 (c) 960 (d) 73
  33. 33.What is the 22nd term of the AP 15, 20, 25, 30, …? (a) 120 (b) 110 (c) 105 (d) 125
  34. 34.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 38 (b) 70 (c) 13 (d) 35
  35. 35.What is the 26th term of the AP 13, 15, 17, 19, …? (a) 50 (b) 65 (c) 52 (d) 63
  36. 36.Which term of the AP 18, 20, 22, 24, … is 76? (a) 38th (b) 31st (c) 29th (d) 30th
  37. 37.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4753 (c) 4851 (d) 4802
  38. 38.What is the 12th term of the AP 13, 21, 29, 37, …? (a) 109 (b) 96 (c) 101 (d) 88
  39. 39.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 33 (b) 26 (c) 27 (d) 28
  40. 40.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 91 (c) 210 (d) 98

Answer key

  1. 35
  2. 841
  3. 75
  4. 27th
  5. 1711
  6. 4371
  7. 169
  8. 60
  9. 14
  10. 729
  11. 55
  12. 144
  13. 384
  14. 900
  15. 250
  16. 243
  17. 16th
  18. 119
  19. 351
  20. 78
  21. 136
  22. 9th
  23. 32nd
  24. 98
  25. 38th
  26. 40
  27. 81
  28. 35
  29. 468
  30. 49
  31. 225
  32. 480
  33. 120
  34. 35
  35. 63
  36. 30th
  37. 4851
  38. 101
  39. 27
  40. 105

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