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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 161 · 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 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 25 (d) 9
  2. 2.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 14 (b) 16 (c) 17 (d) 15
  3. 3.What is the 13th term of the AP 3, 10, 17, 24, …? (a) 87 (b) 91 (c) 94 (d) 84
  4. 4.What is the 32nd term of the AP 4, 12, 20, 28, …? (a) 260 (b) 252 (c) 248 (d) 256
  5. 5.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 18 (b) 9 (c) 10 (d) 11
  6. 6.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 23 (b) 25 (c) 26 (d) 24
  7. 7.What is the 15th term of the AP 11, 15, 19, 23, …? (a) 60 (b) 67 (c) 56 (d) 71
  8. 8.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 26 (b) 7 (c) 25 (d) 50
  9. 9.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3570 (c) 3486 (d) 7140
  10. 10.What is the 38th term of the AP 12, 17, 22, 27, …? (a) 185 (b) 202 (c) 197 (d) 190
  11. 11.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 504 (b) 936 (c) 468 (d) 72
  12. 12.What is the 32nd term of the AP 18, 21, 24, 27, …? (a) 96 (b) 93 (c) 114 (d) 111
  13. 13.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 29 (b) 238 (c) 133 (d) 119
  14. 14.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 24 (b) 25 (c) 27 (d) 23
  15. 15.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 3081 (c) 6320 (d) 3161
  16. 16.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 19 (b) 21 (c) 20 (d) 26
  17. 17.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 20 (b) 19 (c) 21 (d) 23
  18. 18.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  19. 19.Which term of the AP 1, 5, 9, 13, … is 157? (a) 41st (b) 39th (c) 40th (d) 42nd
  20. 20.Which term of the AP 9, 14, 19, 24, … is 129? (a) 25th (b) 24th (c) 27th (d) 26th
  21. 21.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 183 (b) 180 (c) 32 (d) 360
  22. 22.What is the 10th term of the AP 15, 18, 21, 24, …? (a) 30 (b) 27 (c) 45 (d) 42
  23. 23.Which term of the AP 3, 8, 13, 18, … is 153? (a) 33rd (b) 31st (c) 30th (d) 32nd
  24. 24.Which term of the AP 18, 20, 22, 24, … is 84? (a) 33rd (b) 42nd (c) 35th (d) 34th
  25. 25.What is the 35th term of the AP 17, 24, 31, 38, …? (a) 262 (b) 245 (c) 238 (d) 255
  26. 26.What is the 14th term of the AP 10, 14, 18, 22, …? (a) 56 (b) 66 (c) 62 (d) 52
  27. 27.What is the 30th term of the AP 10, 19, 28, 37, …? (a) 280 (b) 271 (c) 261 (d) 270
  28. 28.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
  29. 29.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  30. 30.Which term of the AP 5, 14, 23, 32, … is 329? (a) 39th (b) 36th (c) 37th (d) 38th
  31. 31.What is the 35th term of the AP 14, 22, 30, 38, …? (a) 294 (b) 272 (c) 286 (d) 280
  32. 32.Which term of the AP 8, 17, 26, 35, … is 107? (a) 13th (b) 14th (c) 12th (d) 11th
  33. 33.What is the 16th term of the AP 11, 13, 15, 17, …? (a) 43 (b) 30 (c) 32 (d) 41
  34. 34.What is the 27th term of the AP 19, 22, 25, 28, …? (a) 81 (b) 97 (c) 100 (d) 78
  35. 35.What is the 27th term of the AP 8, 16, 24, 32, …? (a) 208 (b) 224 (c) 217 (d) 216
  36. 36.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 132 (c) 66 (d) 55
  37. 37.Which term of the AP 4, 10, 16, 22, … is 160? (a) 29th (b) 27th (c) 28th (d) 26th
  38. 38.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 24 (b) 26 (c) 29 (d) 25
  39. 39.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 95 (b) 80 (c) 160 (d) 28
  40. 40.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 171 (b) 189 (c) 35 (d) 342

Answer key

  1. 25
  2. 15
  3. 87
  4. 252
  5. 10
  6. 24
  7. 67
  8. 25
  9. 3570
  10. 197
  11. 468
  12. 111
  13. 119
  14. 24
  15. 3160
  16. 20
  17. 20
  18. 576
  19. 40th
  20. 25th
  21. 180
  22. 42
  23. 31st
  24. 34th
  25. 255
  26. 62
  27. 271
  28. 361
  29. 121
  30. 37th
  31. 286
  32. 12th
  33. 41
  34. 97
  35. 216
  36. 66
  37. 27th
  38. 25
  39. 80
  40. 171

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