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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 262 · 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, ?, 30, 39, 48? (a) 20 (b) 30 (c) 22 (d) 21
  2. 2.What is the 18th term of the AP 11, 14, 17, 20, …? (a) 51 (b) 65 (c) 62 (d) 54
  3. 3.What is the 23rd term of the AP 18, 26, 34, 42, …? (a) 202 (b) 194 (c) 184 (d) 176
  4. 4.What is the 15th term of the AP 5, 12, 19, 26, …? (a) 110 (b) 103 (c) 98 (d) 105
  5. 5.What is the 22nd term of the AP 17, 26, 35, 44, …? (a) 198 (b) 189 (c) 206 (d) 215
  6. 6.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 57 (b) 384 (c) 354 (d) 708
  7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
  8. 8.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 56 (d) 49
  9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  10. 10.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 40 (b) 440 (c) 220 (d) 240
  11. 11.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 65 (c) 70 (d) 11
  12. 12.Which term of the AP 1, 7, 13, 19, … is 55? (a) 9th (b) 11th (c) 12th (d) 10th
  13. 13.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 80 (c) 95 (d) 28
  14. 14.Which term of the AP 8, 16, 24, 32, … is 320? (a) 42nd (b) 39th (c) 40th (d) 41st
  15. 15.Which term of the AP 16, 24, 32, 40, … is 152? (a) 19th (b) 18th (c) 20th (d) 17th
  16. 16.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 21 (b) 22 (c) 29 (d) 20
  17. 17.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 306 (b) 162 (c) 25 (d) 153
  18. 18.What is the 36th term of the AP 12, 18, 24, 30, …? (a) 222 (b) 216 (c) 210 (d) 228
  19. 19.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 84 (b) 20 (c) 75 (d) 150
  20. 20.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 465 (c) 450 (d) 435
  21. 21.What is the 40th term of the AP 18, 25, 32, 39, …? (a) 273 (b) 298 (c) 280 (d) 291
  22. 22.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 198 (c) 99 (d) 108
  23. 23.Which term of the AP 11, 20, 29, 38, … is 119? (a) 12th (b) 14th (c) 13th (d) 15th
  24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 121 (d) 132
  25. 25.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 135 (b) 35 (c) 150 (d) 270
  26. 26.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 153 (c) 162 (d) 171
  27. 27.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 105 (d) 27
  28. 28.What is the 15th term of the AP 12, 21, 30, 39, …? (a) 126 (b) 135 (c) 147 (d) 138
  29. 29.What is the 37th term of the AP 4, 12, 20, 28, …? (a) 300 (b) 292 (c) 296 (d) 288
  30. 30.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 18 (b) 150 (c) 300 (d) 156
  31. 31.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 12 (b) 72 (c) 144 (d) 73
  32. 32.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 29 (b) 100 (c) 190 (d) 95
  33. 33.Which term of the AP 3, 11, 19, 27, … is 307? (a) 41st (b) 38th (c) 39th (d) 40th
  34. 34.What is the 15th term of the AP 19, 26, 33, 40, …? (a) 105 (b) 124 (c) 98 (d) 117
  35. 35.What is the 11th term of the AP 3, 10, 17, 24, …? (a) 73 (b) 80 (c) 77 (d) 70
  36. 36.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 279 (b) 306 (c) 55 (d) 558
  37. 37.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 191 (c) 171 (d) 380
  38. 38.What is the 34th term of the AP 6, 11, 16, 21, …? (a) 165 (b) 171 (c) 176 (d) 170
  39. 39.What is the 11th term of the AP 2, 7, 12, 17, …? (a) 57 (b) 55 (c) 50 (d) 52
  40. 40.What is the 10th term of the AP 11, 13, 15, 17, …? (a) 31 (b) 18 (c) 20 (d) 29

Answer key

  1. 21
  2. 62
  3. 194
  4. 103
  5. 206
  6. 354
  7. 36
  8. 49
  9. 625
  10. 220
  11. 65
  12. 10th
  13. 80
  14. 40th
  15. 18th
  16. 21
  17. 153
  18. 222
  19. 75
  20. 465
  21. 291
  22. 99
  23. 13th
  24. 121
  25. 135
  26. 171
  27. 196
  28. 138
  29. 292
  30. 150
  31. 72
  32. 95
  33. 39th
  34. 117
  35. 73
  36. 279
  37. 190
  38. 171
  39. 52
  40. 29

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