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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 142 · 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 11 terms of the AP 2, 5, 8, …? (a) 190 (b) 32 (c) 187 (d) 374
  2. 2.What is the 32nd term of the AP 16, 23, 30, 37, …? (a) 224 (b) 217 (c) 233 (d) 240
  3. 3.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 21 (b) 126 (c) 234 (d) 117
  4. 4.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 20 (b) 21 (c) 25 (d) 19
  5. 5.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 228 (b) 132 (c) 34 (d) 114
  6. 6.What is the 21st term of the AP 6, 8, 10, 12, …? (a) 40 (b) 46 (c) 42 (d) 48
  7. 7.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 300 (c) 326 (d) 650
  8. 8.What is the 21st term of the AP 19, 24, 29, 34, …? (a) 124 (b) 100 (c) 105 (d) 119
  9. 9.What is the 32nd term of the AP 14, 17, 20, 23, …? (a) 110 (b) 107 (c) 93 (d) 96
  10. 10.What is the 20th term of the AP 8, 14, 20, 26, …? (a) 120 (b) 128 (c) 122 (d) 114
  11. 11.What is the 23rd term of the AP 5, 10, 15, 20, …? (a) 116 (b) 115 (c) 110 (d) 120
  12. 12.What is the 38th term of the AP 6, 9, 12, 15, …? (a) 120 (b) 117 (c) 114 (d) 111
  13. 13.What is the missing term in the AP 11, 13, 15, ?, 19? (a) 16 (b) 17 (c) 19 (d) 18
  14. 14.What is the missing term in the AP 15, 24, 33, ?, 51? (a) 42 (b) 43 (c) 41 (d) 51
  15. 15.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 20 (b) 21 (c) 19 (d) 26
  16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 55 (d) 784
  17. 17.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 54 (b) 7 (c) 30 (d) 27
  18. 18.What is the 33rd term of the AP 1, 6, 11, 16, …? (a) 161 (b) 166 (c) 165 (d) 160
  19. 19.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  20. 20.Which term of the AP 6, 15, 24, 33, … is 321? (a) 38th (b) 36th (c) 35th (d) 37th
  21. 21.What is the sum of all the whole numbers from 1 to 95? (a) 4560 (b) 4561 (c) 9120 (d) 4465
  22. 22.What is the missing term in the AP 2, 6, ?, 14, 18? (a) 11 (b) 14 (c) 9 (d) 10
  23. 23.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 144 (b) 30 (c) 128 (d) 256
  24. 24.What is the 10th term of the AP 17, 21, 25, 29, …? (a) 57 (b) 36 (c) 40 (d) 53
  25. 25.What is the 17th term of the AP 13, 16, 19, 22, …? (a) 61 (b) 51 (c) 64 (d) 48
  26. 26.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 17 (d) 45
  27. 27.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 56 (d) 28
  29. 29.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 54 (b) 270 (c) 540 (d) 297
  30. 30.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 112 (b) 224 (c) 31 (d) 117
  31. 31.What is the missing term in the AP 12, 18, ?, 30, 36? (a) 30 (b) 24 (c) 25 (d) 23
  32. 32.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 25 (b) 170 (c) 320 (d) 160
  33. 33.What is the 33rd term of the AP 5, 11, 17, 23, …? (a) 203 (b) 198 (c) 192 (d) 197
  34. 34.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 7 (b) 8 (c) 10 (d) 6
  35. 35.What is the missing term in the AP 17, 20, ?, 26, 29? (a) 26 (b) 24 (c) 22 (d) 23
  36. 36.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2146 (c) 2145 (d) 2080
  37. 37.What is the 36th term of the AP 4, 10, 16, 22, …? (a) 216 (b) 220 (c) 214 (d) 210
  38. 38.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 47 (d) 300
  39. 39.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 20 (b) 21 (c) 24 (d) 22
  40. 40.What is the 28th term of the AP 8, 14, 20, 26, …? (a) 170 (b) 176 (c) 162 (d) 168

Answer key

  1. 187
  2. 233
  3. 117
  4. 20
  5. 114
  6. 46
  7. 325
  8. 119
  9. 107
  10. 122
  11. 115
  12. 117
  13. 17
  14. 42
  15. 20
  16. 784
  17. 27
  18. 161
  19. 36
  20. 36th
  21. 4560
  22. 10
  23. 128
  24. 53
  25. 61
  26. 81
  27. 729
  28. 49
  29. 270
  30. 112
  31. 24
  32. 160
  33. 197
  34. 7
  35. 23
  36. 2145
  37. 214
  38. 576
  39. 21
  40. 170

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