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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 710 · 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 16, ?, 22, 25, 28? (a) 19 (b) 22 (c) 20 (d) 18
  2. 2.What is the 18th term of the AP 3, 5, 7, 9, …? (a) 37 (b) 36 (c) 39 (d) 34
  3. 3.Which term of the AP 15, 17, 19, 21, … is 87? (a) 39th (b) 37th (c) 38th (d) 36th
  4. 4.What is the 15th term of the AP 4, 12, 20, 28, …? (a) 112 (b) 120 (c) 116 (d) 124
  5. 5.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 280 (b) 28 (c) 140 (d) 152
  6. 6.What is the 27th term of the AP 18, 25, 32, 39, …? (a) 182 (b) 189 (c) 207 (d) 200
  7. 7.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 25 (b) 26 (c) 24 (d) 23
  8. 8.What is the 16th term of the AP 12, 15, 18, 21, …? (a) 45 (b) 60 (c) 48 (d) 57
  9. 9.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 256 (b) 23 (c) 128 (d) 136
  10. 10.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 62 (b) 380 (c) 350 (d) 700
  11. 11.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 45 (d) 90
  12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 324 (d) 35
  13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 121 (d) 21
  14. 14.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 14 (b) 7 (c) 9 (d) 8
  15. 15.What is the 37th term of the AP 12, 19, 26, 33, …? (a) 259 (b) 271 (c) 252 (d) 264
  16. 16.What is the 21st term of the AP 12, 17, 22, 27, …? (a) 117 (b) 105 (c) 100 (d) 112
  17. 17.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 4005 (c) 4095 (d) 8190
  18. 18.Which term of the AP 14, 19, 24, 29, … is 59? (a) 12th (b) 10th (c) 11th (d) 9th
  19. 19.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 31 (b) 112 (c) 224 (d) 117
  20. 20.What is the 31st term of the AP 4, 6, 8, 10, …? (a) 64 (b) 62 (c) 60 (d) 66
  21. 21.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 15 (c) 63 (d) 70
  22. 22.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 95 (c) 80 (d) 28
  23. 23.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 4422 (c) 2145 (d) 2178
  24. 24.What is the 19th term of the AP 3, 10, 17, 24, …? (a) 136 (b) 133 (c) 129 (d) 126
  25. 25.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 176 (b) 165 (c) 330 (d) 25
  26. 26.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 4372 (c) 8742 (d) 4278
  27. 27.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 108 (b) 102 (c) 204 (d) 14
  28. 28.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 441 (d) 462
  29. 29.What is the 38th term of the AP 3, 5, 7, 9, …? (a) 77 (b) 79 (c) 76 (d) 74
  30. 30.What is the 10th term of the AP 18, 22, 26, 30, …? (a) 36 (b) 40 (c) 58 (d) 54
  31. 31.Which term of the AP 19, 21, 23, 25, … is 57? (a) 22nd (b) 21st (c) 19th (d) 20th
  32. 32.Which term of the AP 9, 11, 13, 15, … is 31? (a) 13th (b) 14th (c) 11th (d) 12th
  33. 33.Which term of the AP 9, 16, 23, 30, … is 93? (a) 15th (b) 14th (c) 13th (d) 12th
  34. 34.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 16 (b) 17 (c) 18 (d) 24
  35. 35.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 240 (b) 440 (c) 40 (d) 220
  36. 36.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 946 (c) 1980 (d) 968
  37. 37.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 456 (b) 852 (c) 63 (d) 426
  38. 38.What is the 14th term of the AP 9, 16, 23, 30, …? (a) 91 (b) 107 (c) 98 (d) 100
  39. 39.What is the 22nd term of the AP 12, 14, 16, 18, …? (a) 44 (b) 54 (c) 56 (d) 42
  40. 40.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 48 (b) 90 (c) 45 (d) 10

Answer key

  1. 19
  2. 37
  3. 37th
  4. 116
  5. 140
  6. 200
  7. 24
  8. 57
  9. 128
  10. 350
  11. 81
  12. 324
  13. 121
  14. 8
  15. 264
  16. 112
  17. 4095
  18. 10th
  19. 112
  20. 64
  21. 63
  22. 80
  23. 2211
  24. 129
  25. 165
  26. 4371
  27. 102
  28. 441
  29. 77
  30. 54
  31. 20th
  32. 12th
  33. 13th
  34. 17
  35. 220
  36. 990
  37. 426
  38. 100
  39. 54
  40. 45

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