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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 208 · 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 22nd term of the AP 11, 13, 15, 17, …? (a) 42 (b) 44 (c) 53 (d) 55
  2. 2.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 312 (b) 30 (c) 168 (d) 156
  3. 3.What is the 10th term of the AP 20, 27, 34, 41, …? (a) 83 (b) 63 (c) 90 (d) 70
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  5. 5.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  6. 6.Which term of the AP 17, 26, 35, 44, … is 107? (a) 11th (b) 10th (c) 12th (d) 13th
  7. 7.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 80 (b) 72 (c) 144 (d) 16
  8. 8.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 54 (b) 96 (c) 48 (d) 13
  9. 9.What is the 35th term of the AP 6, 9, 12, 15, …? (a) 111 (b) 102 (c) 108 (d) 105
  10. 10.What is the 12th term of the AP 17, 25, 33, 41, …? (a) 113 (b) 96 (c) 105 (d) 88
  11. 11.What is the 35th term of the AP 1, 3, 5, 7, …? (a) 71 (b) 68 (c) 69 (d) 70
  12. 12.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5000 (c) 4950 (d) 5050
  13. 13.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 4290 (c) 2145 (d) 2080
  14. 14.What is the 30th term of the AP 14, 16, 18, 20, …? (a) 74 (b) 72 (c) 60 (d) 58
  15. 15.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 39 (b) 48 (c) 40 (d) 38
  16. 16.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 2556 (c) 5112 (d) 2557
  17. 17.What is the 16th term of the AP 17, 20, 23, 26, …? (a) 48 (b) 62 (c) 65 (d) 45
  18. 18.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 160 (c) 80 (d) 17
  19. 19.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 256 (b) 136 (c) 23 (d) 128
  20. 20.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 702 (c) 676 (d) 51
  21. 21.What is the 13th term of the AP 6, 13, 20, 27, …? (a) 84 (b) 97 (c) 90 (d) 91
  22. 22.What is the sum of all the whole numbers from 1 to 90? (a) 4095 (b) 4005 (c) 8190 (d) 4050
  23. 23.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 92 (c) 182 (d) 91
  24. 24.What is the missing term in the AP 3, 11, 19, ?, 35? (a) 26 (b) 35 (c) 28 (d) 27
  25. 25.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 143 (b) 286 (c) 18 (d) 144
  26. 26.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  27. 27.What is the 35th term of the AP 1, 5, 9, 13, …? (a) 140 (b) 137 (c) 141 (d) 136
  28. 28.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 529 (d) 552
  29. 29.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 16 (b) 9 (c) 8 (d) 10
  30. 30.What is the 12th term of the AP 5, 14, 23, 32, …? (a) 99 (b) 104 (c) 113 (d) 108
  31. 31.Which term of the AP 19, 26, 33, 40, … is 117? (a) 17th (b) 15th (c) 16th (d) 14th
  32. 32.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 23 (b) 24 (c) 22 (d) 21
  33. 33.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 396 (b) 429 (c) 66 (d) 792
  34. 34.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 22 (b) 16 (c) 15 (d) 17
  35. 35.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 253 (d) 484
  36. 36.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 90 (b) 99 (c) 18 (d) 180
  37. 37.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 21 (b) 16 (c) 14 (d) 15
  38. 38.What is the 29th term of the AP 3, 7, 11, 15, …? (a) 112 (b) 116 (c) 115 (d) 119
  39. 39.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 120 (b) 60 (c) 22 (d) 65
  40. 40.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 464 (b) 50 (c) 256 (d) 232

Answer key

  1. 53
  2. 156
  3. 83
  4. 784
  5. 169
  6. 11th
  7. 72
  8. 48
  9. 108
  10. 105
  11. 69
  12. 5050
  13. 2145
  14. 72
  15. 39
  16. 2556
  17. 62
  18. 80
  19. 128
  20. 676
  21. 90
  22. 4095
  23. 91
  24. 27
  25. 143
  26. 900
  27. 137
  28. 529
  29. 9
  30. 104
  31. 15th
  32. 22
  33. 396
  34. 16
  35. 484
  36. 90
  37. 15
  38. 115
  39. 60
  40. 232

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