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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 769 · 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 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 17 (d) 45
  2. 2.What is the 35th term of the AP 2, 9, 16, 23, …? (a) 247 (b) 238 (c) 245 (d) 240
  3. 3.What is the 36th term of the AP 20, 26, 32, 38, …? (a) 216 (b) 210 (c) 236 (d) 230
  4. 4.What is the 16th term of the AP 6, 11, 16, 21, …? (a) 80 (b) 81 (c) 75 (d) 86
  5. 5.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 21 (b) 18 (c) 16 (d) 17
  6. 6.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 18 (b) 50 (c) 60 (d) 100
  7. 7.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  8. 8.Which term of the AP 5, 10, 15, 20, … is 155? (a) 32nd (b) 33rd (c) 30th (d) 31st
  9. 9.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3403 (c) 3362 (d) 3321
  10. 10.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 8 (b) 10 (c) 7 (d) 6
  11. 11.What is the 17th term of the AP 20, 26, 32, 38, …? (a) 96 (b) 122 (c) 102 (d) 116
  12. 12.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 276 (c) 277 (d) 552
  13. 13.What is the 22nd term of the AP 11, 14, 17, 20, …? (a) 77 (b) 74 (c) 66 (d) 63
  14. 14.What is the 40th term of the AP 17, 24, 31, 38, …? (a) 273 (b) 290 (c) 297 (d) 280
  15. 15.What is the 11th term of the AP 20, 26, 32, 38, …? (a) 86 (b) 66 (c) 60 (d) 80
  16. 16.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 14 (b) 16 (c) 20 (d) 15
  17. 17.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 80 (b) 160 (c) 85 (d) 26
  18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  19. 19.Which term of the AP 16, 20, 24, 28, … is 100? (a) 23rd (b) 21st (c) 22nd (d) 25th
  20. 20.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 12 (c) 114 (d) 60
  21. 21.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 136 (d) 272
  22. 22.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 16 (b) 60 (c) 65 (d) 120
  23. 23.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 190 (c) 380 (d) 171
  24. 24.What is the 39th term of the AP 19, 27, 35, 43, …? (a) 323 (b) 304 (c) 312 (d) 331
  25. 25.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3698 (c) 7482 (d) 3741
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 72 (d) 15
  27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 9 (d) 30
  28. 28.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 108 (b) 19 (c) 99 (d) 198
  29. 29.Which term of the AP 6, 11, 16, 21, … is 81? (a) 17th (b) 18th (c) 16th (d) 15th
  30. 30.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 216 (b) 396 (c) 38 (d) 198
  31. 31.What is the 37th term of the AP 12, 16, 20, 24, …? (a) 160 (b) 148 (c) 144 (d) 156
  32. 32.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 6 (b) 5 (c) 4 (d) 3
  33. 33.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 11 (b) 13 (c) 18 (d) 12
  34. 34.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 17 (b) 26 (c) 19 (d) 18
  35. 35.What is the 39th term of the AP 1, 4, 7, 10, …? (a) 118 (b) 115 (c) 114 (d) 117
  36. 36.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 406 (d) 784
  37. 37.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 154 (d) 306
  38. 38.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 93 (b) 186 (c) 23 (d) 102
  39. 39.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 27 (b) 29 (c) 25 (d) 26
  40. 40.Which term of the AP 19, 21, 23, 25, … is 47? (a) 14th (b) 17th (c) 15th (d) 16th

Answer key

  1. 81
  2. 240
  3. 230
  4. 81
  5. 17
  6. 50
  7. 121
  8. 31st
  9. 3403
  10. 7
  11. 116
  12. 276
  13. 74
  14. 290
  15. 80
  16. 15
  17. 80
  18. 841
  19. 22nd
  20. 57
  21. 256
  22. 60
  23. 190
  24. 323
  25. 3741
  26. 64
  27. 25
  28. 99
  29. 16th
  30. 198
  31. 156
  32. 4
  33. 12
  34. 18
  35. 115
  36. 784
  37. 153
  38. 93
  39. 26
  40. 15th

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