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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 774 · 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 terms of the AP 7, 8, 9, …? (a) 198 (b) 99 (c) 15 (d) 100
  2. 2.What is the 34th term of the AP 19, 21, 23, 25, …? (a) 66 (b) 68 (c) 87 (d) 85
  3. 3.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 55 (c) 100 (d) 50
  4. 4.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 135 (b) 270 (c) 150 (d) 35
  5. 5.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 22 (b) 23 (c) 21 (d) 30
  6. 6.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 286 (b) 46 (c) 572 (d) 308
  7. 7.What is the 30th term of the AP 3, 8, 13, 18, …? (a) 153 (b) 145 (c) 148 (d) 150
  8. 8.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 528 (b) 984 (c) 74 (d) 492
  9. 9.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28
  10. 10.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3240 (c) 6642 (d) 3321
  11. 11.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 91 (c) 180 (d) 90
  12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 35 (d) 171
  13. 13.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 95 (c) 28 (d) 80
  14. 14.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 12 (b) 100 (c) 50 (d) 51
  15. 15.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 29 (b) 198 (c) 99 (d) 114
  16. 16.What is the 34th term of the AP 8, 13, 18, 23, …? (a) 170 (b) 165 (c) 173 (d) 178
  17. 17.Which term of the AP 12, 17, 22, 27, … is 172? (a) 35th (b) 33rd (c) 34th (d) 32nd
  18. 18.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 14 (b) 15 (c) 16 (d) 19
  19. 19.What is the 14th term of the AP 14, 20, 26, 32, …? (a) 98 (b) 84 (c) 78 (d) 92
  20. 20.What is the 39th term of the AP 15, 17, 19, 21, …? (a) 78 (b) 93 (c) 76 (d) 91
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 11 (d) 42
  22. 22.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 384 (b) 192 (c) 204 (d) 27
  23. 23.Which term of the AP 19, 27, 35, 43, … is 187? (a) 24th (b) 21st (c) 22nd (d) 23rd
  24. 24.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 216 (b) 126 (c) 33 (d) 108
  25. 25.What is the 10th term of the AP 5, 7, 9, 11, …? (a) 25 (b) 18 (c) 23 (d) 20
  26. 26.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 71 (b) 13 (c) 140 (d) 70
  27. 27.Which term of the AP 6, 10, 14, 18, … is 126? (a) 31st (b) 30th (c) 33rd (d) 32nd
  28. 28.Which term of the AP 11, 17, 23, 29, … is 149? (a) 23rd (b) 24th (c) 26th (d) 25th
  29. 29.What is the missing term in the AP 4, 8, ?, 16, 20? (a) 11 (b) 16 (c) 12 (d) 13
  30. 30.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 14 (b) 15 (c) 16 (d) 18
  31. 31.Which term of the AP 13, 18, 23, 28, … is 48? (a) 9th (b) 7th (c) 10th (d) 8th
  32. 32.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 66 (c) 72 (d) 78
  33. 33.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 279 (b) 504 (c) 252 (d) 52
  34. 34.What is the 10th term of the AP 11, 14, 17, 20, …? (a) 41 (b) 38 (c) 27 (d) 30
  35. 35.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 55 (d) 110
  36. 36.What is the 40th term of the AP 7, 12, 17, 22, …? (a) 207 (b) 202 (c) 195 (d) 200
  37. 37.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 216 (b) 28 (c) 408 (d) 204
  38. 38.What is the 30th term of the AP 7, 13, 19, 25, …? (a) 187 (b) 181 (c) 180 (d) 174
  39. 39.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 96 (c) 192 (d) 114
  40. 40.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 22 (b) 65 (c) 60 (d) 120

Answer key

  1. 99
  2. 85
  3. 50
  4. 135
  5. 22
  6. 286
  7. 148
  8. 492
  9. 49
  10. 3321
  11. 90
  12. 324
  13. 80
  14. 50
  15. 99
  16. 173
  17. 33rd
  18. 15
  19. 92
  20. 91
  21. 36
  22. 192
  23. 22nd
  24. 108
  25. 23
  26. 70
  27. 31st
  28. 24th
  29. 12
  30. 15
  31. 8th
  32. 78
  33. 252
  34. 38
  35. 55
  36. 202
  37. 204
  38. 181
  39. 96
  40. 60

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