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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 684 · 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 14th term of the AP 11, 19, 27, 35, …? (a) 104 (b) 112 (c) 123 (d) 115
  2. 2.What is the 33rd term of the AP 7, 13, 19, 25, …? (a) 192 (b) 205 (c) 198 (d) 199
  3. 3.What is the 21st term of the AP 12, 14, 16, 18, …? (a) 42 (b) 54 (c) 52 (d) 40
  4. 4.What is the 11th term of the AP 4, 7, 10, 13, …? (a) 30 (b) 33 (c) 34 (d) 37
  5. 5.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 132 (b) 66 (c) 67 (d) 11
  6. 6.What is the 16th term of the AP 5, 13, 21, 29, …? (a) 120 (b) 128 (c) 133 (d) 125
  7. 7.What is the 30th term of the AP 13, 17, 21, 25, …? (a) 129 (b) 116 (c) 133 (d) 120
  8. 8.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 1406 (c) 703 (d) 666
  9. 9.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 84 (b) 168 (c) 85 (d) 15
  10. 10.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  11. 11.What is the 39th term of the AP 5, 8, 11, 14, …? (a) 114 (b) 119 (c) 122 (d) 117
  12. 12.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 171 (d) 153
  13. 13.What is the 30th term of the AP 13, 21, 29, 37, …? (a) 253 (b) 240 (c) 245 (d) 232
  14. 14.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 240 (b) 45 (c) 220 (d) 440
  15. 15.What is the 17th term of the AP 7, 15, 23, 31, …? (a) 135 (b) 143 (c) 128 (d) 136
  16. 16.Which term of the AP 3, 6, 9, 12, … is 108? (a) 38th (b) 37th (c) 36th (d) 35th
  17. 17.What is the missing term in the AP 14, 23, ?, 41, 50? (a) 41 (b) 32 (c) 31 (d) 33
  18. 18.What is the 17th term of the AP 7, 11, 15, 19, …? (a) 64 (b) 75 (c) 68 (d) 71
  19. 19.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 22 (b) 24 (c) 26 (d) 23
  20. 20.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 286 (b) 291 (c) 572 (d) 51
  21. 21.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 120 (c) 105 (d) 240
  22. 22.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3403 (c) 3487 (d) 3486
  23. 23.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 6320 (c) 3081 (d) 3161
  24. 24.What is the 17th term of the AP 11, 19, 27, 35, …? (a) 136 (b) 128 (c) 139 (d) 147
  25. 25.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 10 (b) 9 (c) 8 (d) 11
  26. 26.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 700 (b) 62 (c) 350 (d) 380
  27. 27.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 28 (b) 29 (c) 7 (d) 56
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28
  29. 29.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4656 (c) 4754 (d) 4753
  30. 30.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 9 (c) 42 (d) 84
  31. 31.What is the 28th term of the AP 6, 12, 18, 24, …? (a) 174 (b) 162 (c) 169 (d) 168
  32. 32.What is the 36th term of the AP 6, 8, 10, 12, …? (a) 72 (b) 70 (c) 76 (d) 78
  33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  34. 34.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 600 (c) 300 (d) 330
  35. 35.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 100 (b) 16 (c) 104 (d) 200
  36. 36.What is the 27th term of the AP 10, 15, 20, 25, …? (a) 140 (b) 130 (c) 145 (d) 135
  37. 37.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  38. 38.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 22 (b) 84 (c) 72 (d) 144
  39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 9 (d) 30
  40. 40.What is the 20th term of the AP 10, 16, 22, 28, …? (a) 124 (b) 130 (c) 114 (d) 120

Answer key

  1. 115
  2. 199
  3. 52
  4. 34
  5. 66
  6. 125
  7. 129
  8. 703
  9. 84
  10. 324
  11. 119
  12. 171
  13. 245
  14. 220
  15. 135
  16. 36th
  17. 32
  18. 71
  19. 23
  20. 286
  21. 120
  22. 3486
  23. 3160
  24. 139
  25. 9
  26. 350
  27. 28
  28. 49
  29. 4753
  30. 42
  31. 168
  32. 76
  33. 361
  34. 300
  35. 100
  36. 140
  37. 91
  38. 72
  39. 25
  40. 124

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