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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 386 · 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 25th term of the AP 2, 5, 8, 11, …? (a) 74 (b) 72 (c) 77 (d) 75
  2. 2.What is the 38th term of the AP 2, 7, 12, 17, …? (a) 187 (b) 192 (c) 190 (d) 185
  3. 3.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 4950 (c) 5050 (d) 10100
  4. 4.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 153 (b) 288 (c) 144 (d) 24
  5. 5.What is the 24th term of the AP 4, 10, 16, 22, …? (a) 142 (b) 148 (c) 144 (d) 138
  6. 6.What is the 33rd term of the AP 16, 19, 22, 25, …? (a) 115 (b) 96 (c) 99 (d) 112
  7. 7.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 720 (b) 52 (c) 360 (d) 384
  8. 8.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 24 (b) 25 (c) 29 (d) 23
  9. 9.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1036 (c) 2070 (d) 1035
  10. 10.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 26 (b) 352 (c) 176 (d) 187
  11. 11.What is the 29th term of the AP 12, 19, 26, 33, …? (a) 203 (b) 196 (c) 208 (d) 215
  12. 12.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 11 (b) 13 (c) 12 (d) 10
  13. 13.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 171 (b) 342 (c) 35 (d) 189
  14. 14.What is the 40th term of the AP 14, 18, 22, 26, …? (a) 156 (b) 174 (c) 170 (d) 160
  15. 15.Which term of the AP 12, 15, 18, 21, … is 117? (a) 37th (b) 35th (c) 36th (d) 39th
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  17. 17.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 53 (b) 616 (c) 313 (d) 308
  18. 18.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 270 (b) 27 (c) 135 (d) 138
  19. 19.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 132 (b) 242 (c) 21 (d) 121
  20. 20.What is the 12th term of the AP 2, 5, 8, 11, …? (a) 35 (b) 36 (c) 38 (d) 33
  21. 21.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 22 (b) 84 (c) 72 (d) 144
  22. 22.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 130 (c) 240 (d) 21
  23. 23.Which term of the AP 18, 23, 28, 33, … is 213? (a) 40th (b) 41st (c) 42nd (d) 39th
  24. 24.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 5256 (c) 2592 (d) 2628
  25. 25.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 140 (b) 70 (c) 16 (d) 77
  26. 26.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 58 (b) 306 (c) 333 (d) 612
  27. 27.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2016 (c) 2048 (d) 2080
  28. 28.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 220 (b) 231 (c) 30 (d) 440
  29. 29.What is the 33rd term of the AP 6, 12, 18, 24, …? (a) 199 (b) 198 (c) 192 (d) 204
  30. 30.What is the 38th term of the AP 6, 8, 10, 12, …? (a) 74 (b) 82 (c) 76 (d) 80
  31. 31.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 272 (d) 256
  32. 32.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1378 (c) 1326 (d) 1352
  33. 33.What is the 39th term of the AP 11, 13, 15, 17, …? (a) 78 (b) 87 (c) 76 (d) 89
  34. 34.What is the 13th term of the AP 1, 4, 7, 10, …? (a) 36 (b) 39 (c) 40 (d) 37
  35. 35.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 496 (d) 1056
  36. 36.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 306 (b) 33 (c) 171 (d) 153
  37. 37.What is the 19th term of the AP 5, 13, 21, 29, …? (a) 149 (b) 144 (c) 157 (d) 152
  38. 38.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 22 (b) 24 (c) 20 (d) 21
  39. 39.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 16 (b) 12 (c) 13 (d) 11
  40. 40.What is the 29th term of the AP 13, 16, 19, 22, …? (a) 84 (b) 97 (c) 87 (d) 100

Answer key

  1. 74
  2. 187
  3. 5050
  4. 144
  5. 142
  6. 112
  7. 360
  8. 24
  9. 1035
  10. 176
  11. 208
  12. 11
  13. 171
  14. 170
  15. 36th
  16. 729
  17. 308
  18. 135
  19. 121
  20. 35
  21. 72
  22. 120
  23. 40th
  24. 2628
  25. 70
  26. 306
  27. 2080
  28. 220
  29. 198
  30. 80
  31. 256
  32. 1378
  33. 87
  34. 37
  35. 528
  36. 153
  37. 149
  38. 21
  39. 12
  40. 97

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