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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 354 · 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 12, ?, 20, 24, 28? (a) 20 (b) 15 (c) 17 (d) 16
  2. 2.What is the 13th term of the AP 18, 24, 30, 36, …? (a) 72 (b) 96 (c) 90 (d) 78
  3. 3.What is the 10th term of the AP 3, 10, 17, 24, …? (a) 70 (b) 66 (c) 73 (d) 63
  4. 4.Which term of the AP 4, 9, 14, 19, … is 64? (a) 12th (b) 13th (c) 14th (d) 15th
  5. 5.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 240 (d) 120
  6. 6.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 380 (c) 37 (d) 190
  7. 7.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 861 (c) 882 (d) 903
  8. 8.What is the 28th term of the AP 1, 5, 9, 13, …? (a) 112 (b) 108 (c) 109 (d) 113
  9. 9.What is the 32nd term of the AP 5, 10, 15, 20, …? (a) 160 (b) 155 (c) 165 (d) 161
  10. 10.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 42 (c) 36 (d) 11
  11. 11.What is the missing term in the AP 20, 27, 34, ?, 48? (a) 40 (b) 48 (c) 41 (d) 42
  12. 12.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 203 (b) 396 (c) 198 (d) 42
  13. 13.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 28 (b) 147 (c) 288 (d) 144
  14. 14.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 378 (d) 756
  15. 15.What is the 14th term of the AP 10, 17, 24, 31, …? (a) 108 (b) 98 (c) 91 (d) 101
  16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  17. 17.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 225 (b) 39 (c) 414 (d) 207
  18. 18.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 228 (b) 15 (c) 120 (d) 114
  19. 19.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 43 (b) 38 (c) 36 (d) 37
  20. 20.What is the 11th term of the AP 3, 8, 13, 18, …? (a) 58 (b) 53 (c) 55 (d) 50
  21. 21.What is the 38th term of the AP 18, 20, 22, 24, …? (a) 92 (b) 76 (c) 74 (d) 94
  22. 22.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 190 (b) 100 (c) 29 (d) 95
  23. 23.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1225 (c) 1275 (d) 1250
  24. 24.What is the 13th term of the AP 9, 11, 13, 15, …? (a) 33 (b) 35 (c) 26 (d) 24
  25. 25.Which term of the AP 19, 23, 27, 31, … is 155? (a) 36th (b) 37th (c) 35th (d) 34th
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 256 (c) 31 (d) 136
  27. 27.What is the 25th term of the AP 14, 22, 30, 38, …? (a) 200 (b) 214 (c) 192 (d) 206
  28. 28.What is the 30th term of the AP 13, 17, 21, 25, …? (a) 133 (b) 116 (c) 129 (d) 120
  29. 29.What is the 30th term of the AP 9, 13, 17, 21, …? (a) 116 (b) 120 (c) 125 (d) 129
  30. 30.What is the 36th term of the AP 5, 10, 15, 20, …? (a) 175 (b) 185 (c) 181 (d) 180
  31. 31.Which term of the AP 4, 7, 10, 13, … is 118? (a) 38th (b) 40th (c) 39th (d) 41st
  32. 32.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 650 (d) 325
  33. 33.What is the 20th term of the AP 10, 17, 24, 31, …? (a) 133 (b) 143 (c) 140 (d) 150
  34. 34.What is the 17th term of the AP 2, 10, 18, 26, …? (a) 136 (b) 128 (c) 138 (d) 130
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  36. 36.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 512 (c) 1056 (d) 528
  37. 37.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 200 (b) 400 (c) 224 (d) 46
  38. 38.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 9312 (c) 4656 (d) 4560
  39. 39.What is the 39th term of the AP 1, 9, 17, 25, …? (a) 312 (b) 313 (c) 304 (d) 305
  40. 40.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 238 (b) 29 (c) 119 (d) 133

Answer key

  1. 16
  2. 90
  3. 66
  4. 13th
  5. 120
  6. 361
  7. 903
  8. 109
  9. 160
  10. 36
  11. 41
  12. 198
  13. 144
  14. 378
  15. 101
  16. 784
  17. 207
  18. 114
  19. 37
  20. 53
  21. 92
  22. 95
  23. 1275
  24. 33
  25. 35th
  26. 256
  27. 206
  28. 129
  29. 125
  30. 180
  31. 39th
  32. 625
  33. 143
  34. 130
  35. 100
  36. 528
  37. 200
  38. 4656
  39. 305
  40. 119

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