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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 340 · 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 6 terms of the AP 3, 5, 7, …? (a) 48 (b) 96 (c) 54 (d) 13
  2. 2.What is the 16th term of the AP 19, 26, 33, 40, …? (a) 131 (b) 105 (c) 124 (d) 112
  3. 3.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 189 (b) 42 (c) 168 (d) 336
  4. 4.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 17 (b) 144 (c) 138 (d) 276
  5. 5.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 440 (b) 67 (c) 407 (d) 814
  6. 6.What is the 20th term of the AP 1, 3, 5, 7, …? (a) 40 (b) 38 (c) 39 (d) 41
  7. 7.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 174 (c) 87 (d) 27
  8. 8.What is the 34th term of the AP 18, 25, 32, 39, …? (a) 238 (b) 249 (c) 256 (d) 231
  9. 9.What is the 36th term of the AP 20, 22, 24, 26, …? (a) 72 (b) 92 (c) 90 (d) 70
  10. 10.Which term of the AP 5, 12, 19, 26, … is 250? (a) 37th (b) 38th (c) 35th (d) 36th
  11. 11.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 2 (b) 4 (c) 5 (d) 3
  12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  13. 13.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  14. 14.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 27 (b) 25 (c) 30 (d) 26
  15. 15.Which term of the AP 3, 9, 15, 21, … is 111? (a) 20th (b) 19th (c) 18th (d) 21st
  16. 16.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 210 (d) 400
  17. 17.What is the 15th term of the AP 11, 20, 29, 38, …? (a) 135 (b) 126 (c) 137 (d) 146
  18. 18.Which term of the AP 6, 10, 14, 18, … is 158? (a) 38th (b) 40th (c) 41st (d) 39th
  19. 19.What is the 14th term of the AP 3, 8, 13, 18, …? (a) 65 (b) 70 (c) 68 (d) 73
  20. 20.What is the 34th term of the AP 1, 9, 17, 25, …? (a) 272 (b) 273 (c) 264 (d) 265
  21. 21.What is the 39th term of the AP 19, 25, 31, 37, …? (a) 253 (b) 234 (c) 247 (d) 228
  22. 22.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 418 (b) 209 (c) 34 (d) 212
  23. 23.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 3192 (c) 1540 (d) 1568
  24. 24.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 11 (c) 35 (d) 70
  25. 25.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 42 (b) 32 (c) 34 (d) 33
  26. 26.Which term of the AP 4, 9, 14, 19, … is 179? (a) 36th (b) 38th (c) 35th (d) 37th
  27. 27.Which term of the AP 1, 3, 5, 7, … is 25? (a) 15th (b) 13th (c) 14th (d) 12th
  28. 28.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 111 (b) 220 (c) 15 (d) 110
  29. 29.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 14 (b) 16 (c) 12 (d) 13
  30. 30.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  31. 31.What is the 28th term of the AP 9, 13, 17, 21, …? (a) 121 (b) 108 (c) 112 (d) 117
  32. 32.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 20 (b) 19 (c) 28 (d) 21
  33. 33.What is the 20th term of the AP 1, 4, 7, 10, …? (a) 57 (b) 61 (c) 60 (d) 58
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  35. 35.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 190 (c) 191 (d) 380
  36. 36.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 21 (b) 168 (c) 84 (d) 87
  37. 37.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 24 (b) 25 (c) 23 (d) 31
  38. 38.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 8 (c) 70 (d) 35
  39. 39.What is the 26th term of the AP 1, 6, 11, 16, …? (a) 131 (b) 130 (c) 125 (d) 126
  40. 40.What is the 37th term of the AP 19, 24, 29, 34, …? (a) 199 (b) 180 (c) 185 (d) 204

Answer key

  1. 48
  2. 124
  3. 168
  4. 138
  5. 407
  6. 39
  7. 87
  8. 249
  9. 90
  10. 36th
  11. 3
  12. 169
  13. 256
  14. 26
  15. 19th
  16. 400
  17. 137
  18. 39th
  19. 68
  20. 265
  21. 247
  22. 209
  23. 1596
  24. 35
  25. 33
  26. 36th
  27. 13th
  28. 110
  29. 13
  30. 196
  31. 117
  32. 20
  33. 58
  34. 25
  35. 190
  36. 84
  37. 24
  38. 35
  39. 126
  40. 199

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