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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 169 · 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 11th term of the AP 2, 6, 10, 14, …? (a) 42 (b) 44 (c) 46 (d) 40
  2. 2.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 21 (b) 242 (c) 132 (d) 121
  3. 3.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 22 (b) 28 (c) 21 (d) 20
  4. 4.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 8 (b) 7 (c) 9 (d) 13
  5. 5.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 18 (b) 84 (c) 78 (d) 156
  6. 6.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 23 (b) 90 (c) 78 (d) 156
  7. 7.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 29 (b) 240 (c) 136 (d) 120
  8. 8.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 160 (b) 83 (c) 22 (d) 80
  9. 9.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4372 (c) 8742 (d) 4371
  10. 10.What is the 30th term of the AP 10, 14, 18, 22, …? (a) 130 (b) 120 (c) 116 (d) 126
  11. 11.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 132 (c) 66 (d) 67
  12. 12.What is the 21st term of the AP 13, 15, 17, 19, …? (a) 55 (b) 40 (c) 53 (d) 42
  13. 13.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 290 (b) 150 (c) 19 (d) 145
  14. 14.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 160 (b) 90 (c) 80 (d) 24
  15. 15.What is the 28th term of the AP 1, 6, 11, 16, …? (a) 140 (b) 136 (c) 135 (d) 141
  16. 16.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 50 (b) 43 (c) 42 (d) 41
  17. 17.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 14 (b) 13 (c) 17 (d) 15
  18. 18.Which term of the AP 2, 4, 6, 8, … is 20? (a) 11th (b) 9th (c) 10th (d) 12th
  19. 19.What is the 10th term of the AP 6, 13, 20, 27, …? (a) 70 (b) 63 (c) 69 (d) 76
  20. 20.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 22 (b) 112 (c) 119 (d) 224
  21. 21.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 42 (b) 44 (c) 43 (d) 51
  22. 22.What is the 39th term of the AP 15, 21, 27, 33, …? (a) 228 (b) 243 (c) 234 (d) 249
  23. 23.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 56 (b) 580 (c) 320 (d) 290
  24. 24.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 650 (d) 300
  25. 25.What is the 14th term of the AP 1, 6, 11, 16, …? (a) 70 (b) 66 (c) 65 (d) 71
  26. 26.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 516 (b) 73 (c) 480 (d) 960
  27. 27.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 180 (b) 18 (c) 90 (d) 99
  28. 28.What is the 21st term of the AP 3, 5, 7, 9, …? (a) 42 (b) 40 (c) 45 (d) 43
  29. 29.What is the 11th term of the AP 3, 11, 19, 27, …? (a) 80 (b) 91 (c) 83 (d) 88
  30. 30.What is the 16th term of the AP 10, 15, 20, 25, …? (a) 80 (b) 85 (c) 75 (d) 90
  31. 31.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 36 (c) 35 (d) 9
  32. 32.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 280 (b) 38 (c) 161 (d) 140
  33. 33.What is the 29th term of the AP 8, 13, 18, 23, …? (a) 148 (b) 153 (c) 145 (d) 140
  34. 34.What is the 15th term of the AP 17, 21, 25, 29, …? (a) 77 (b) 60 (c) 56 (d) 73
  35. 35.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 6 (b) 7 (c) 5 (d) 4
  36. 36.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 28 (b) 23 (c) 24 (d) 25
  37. 37.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 21 (b) 20 (c) 19 (d) 18
  38. 38.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 512 (c) 528 (d) 496
  39. 39.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4465 (c) 9120 (d) 4561
  40. 40.Which term of the AP 12, 14, 16, 18, … is 84? (a) 36th (b) 37th (c) 38th (d) 42nd

Answer key

  1. 42
  2. 121
  3. 21
  4. 8
  5. 78
  6. 78
  7. 120
  8. 80
  9. 4371
  10. 126
  11. 66
  12. 53
  13. 145
  14. 80
  15. 136
  16. 42
  17. 14
  18. 10th
  19. 69
  20. 112
  21. 43
  22. 243
  23. 290
  24. 325
  25. 66
  26. 480
  27. 90
  28. 43
  29. 83
  30. 85
  31. 35
  32. 140
  33. 148
  34. 73
  35. 5
  36. 24
  37. 19
  38. 528
  39. 4560
  40. 37th

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