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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 484 · 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 21st term of the AP 12, 21, 30, 39, …? (a) 180 (b) 189 (c) 192 (d) 201
  2. 2.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 5000 (c) 4950 (d) 10100
  3. 3.What is the 34th term of the AP 13, 16, 19, 22, …? (a) 99 (b) 102 (c) 112 (d) 115
  4. 4.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 1485 (c) 1541 (d) 3080
  5. 5.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 42 (b) 78 (c) 39 (d) 9
  6. 6.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 279 (b) 55 (c) 306 (d) 558
  7. 7.What is the 20th term of the AP 7, 9, 11, 13, …? (a) 47 (b) 38 (c) 45 (d) 40
  8. 8.What is the 28th term of the AP 3, 6, 9, 12, …? (a) 87 (b) 84 (c) 81 (d) 85
  9. 9.Which term of the AP 19, 26, 33, 40, … is 264? (a) 38th (b) 37th (c) 35th (d) 36th
  10. 10.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 340 (b) 180 (c) 170 (d) 26
  11. 11.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 90 (c) 20 (d) 180
  12. 12.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 49 (c) 650 (d) 325
  13. 13.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 96 (c) 48 (d) 54
  14. 14.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1129 (c) 1081 (d) 1128
  15. 15.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 198 (c) 19 (d) 108
  16. 16.What is the 31st term of the AP 10, 16, 22, 28, …? (a) 190 (b) 186 (c) 180 (d) 196
  17. 17.Which term of the AP 3, 9, 15, 21, … is 87? (a) 14th (b) 17th (c) 16th (d) 15th
  18. 18.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 156 (c) 66 (d) 78
  19. 19.Which term of the AP 4, 8, 12, 16, … is 128? (a) 34th (b) 33rd (c) 32nd (d) 31st
  20. 20.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 9 (b) 17 (c) 10 (d) 8
  21. 21.Which term of the AP 6, 12, 18, 24, … is 78? (a) 13th (b) 14th (c) 15th (d) 12th
  22. 22.What is the missing term in the AP 19, 21, 23, ?, 27? (a) 24 (b) 26 (c) 27 (d) 25
  23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 15 (d) 36
  24. 24.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 37 (b) 235 (c) 250 (d) 470
  25. 25.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 4556 (c) 2278 (d) 2279
  26. 26.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 903 (c) 946 (d) 947
  27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  28. 28.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 63 (b) 720 (c) 390 (d) 360
  29. 29.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 336 (b) 48 (c) 624 (d) 312
  30. 30.What is the 37th term of the AP 13, 20, 27, 34, …? (a) 252 (b) 272 (c) 259 (d) 265
  31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 90 (d) 81
  32. 32.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 297 (c) 594 (d) 302
  33. 33.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 19 (b) 25 (c) 17 (d) 18
  34. 34.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 120 (b) 128 (c) 22 (d) 240
  35. 35.What is the 16th term of the AP 13, 20, 27, 34, …? (a) 118 (b) 112 (c) 125 (d) 105
  36. 36.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 990 (c) 968 (d) 946
  37. 37.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 44 (b) 182 (c) 364 (d) 203
  38. 38.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 31 (b) 30 (c) 29 (d) 38
  39. 39.What is the 29th term of the AP 4, 8, 12, 16, …? (a) 117 (b) 112 (c) 116 (d) 120
  40. 40.What is the 16th term of the AP 11, 14, 17, 20, …? (a) 56 (b) 59 (c) 48 (d) 45

Answer key

  1. 192
  2. 5050
  3. 112
  4. 1540
  5. 39
  6. 279
  7. 45
  8. 84
  9. 36th
  10. 170
  11. 90
  12. 625
  13. 48
  14. 1128
  15. 99
  16. 190
  17. 15th
  18. 78
  19. 32nd
  20. 9
  21. 13th
  22. 25
  23. 64
  24. 235
  25. 2278
  26. 946
  27. 100
  28. 360
  29. 312
  30. 265
  31. 81
  32. 297
  33. 18
  34. 120
  35. 118
  36. 990
  37. 182
  38. 30
  39. 116
  40. 56

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