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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 22 · 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 all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 92 (d) 91
  2. 2.What is the 26th term of the AP 17, 22, 27, 32, …? (a) 147 (b) 130 (c) 125 (d) 142
  3. 3.What is the 16th term of the AP 13, 16, 19, 22, …? (a) 48 (b) 61 (c) 45 (d) 58
  4. 4.What is the 17th term of the AP 5, 10, 15, 20, …? (a) 85 (b) 80 (c) 90 (d) 86
  5. 5.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 48 (b) 504 (c) 252 (d) 257
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
  7. 7.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 22 (b) 21 (c) 20 (d) 24
  8. 8.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 984 (b) 74 (c) 492 (d) 528
  9. 9.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 55 (b) 279 (c) 558 (d) 306
  10. 10.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 10 (c) 55 (d) 110
  11. 11.Which term of the AP 6, 12, 18, 24, … is 60? (a) 11th (b) 12th (c) 9th (d) 10th
  12. 12.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 576 (d) 600
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  14. 14.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 16 (b) 17 (c) 15 (d) 18
  15. 15.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 171 (c) 153 (d) 162
  16. 16.What is the missing term in the AP 13, 21, ?, 37, 45? (a) 28 (b) 37 (c) 29 (d) 30
  17. 17.What is the 35th term of the AP 18, 27, 36, 45, …? (a) 333 (b) 306 (c) 315 (d) 324
  18. 18.What is the 29th term of the AP 16, 22, 28, 34, …? (a) 190 (b) 168 (c) 184 (d) 174
  19. 19.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 67 (c) 132 (d) 66
  20. 20.Which term of the AP 12, 17, 22, 27, … is 187? (a) 35th (b) 37th (c) 38th (d) 36th
  21. 21.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 21 (b) 117 (c) 126 (d) 234
  22. 22.Which term of the AP 8, 14, 20, 26, … is 80? (a) 14th (b) 13th (c) 12th (d) 15th
  23. 23.What is the missing term in the AP 9, 14, ?, 24, 29? (a) 18 (b) 19 (c) 20 (d) 24
  24. 24.What is the 31st term of the AP 8, 17, 26, 35, …? (a) 287 (b) 278 (c) 279 (d) 270
  25. 25.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 111 (b) 31 (c) 126 (d) 222
  26. 26.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 80 (b) 70 (c) 140 (d) 22
  27. 27.What is the 16th term of the AP 13, 15, 17, 19, …? (a) 30 (b) 32 (c) 43 (d) 45
  28. 28.What is the 16th term of the AP 16, 21, 26, 31, …? (a) 91 (b) 80 (c) 75 (d) 96
  29. 29.What is the 12th term of the AP 6, 10, 14, 18, …? (a) 50 (b) 44 (c) 54 (d) 48
  30. 30.What is the 12th term of the AP 9, 16, 23, 30, …? (a) 77 (b) 86 (c) 84 (d) 93
  31. 31.What is the 18th term of the AP 8, 10, 12, 14, …? (a) 34 (b) 42 (c) 44 (d) 36
  32. 32.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 260 (b) 140 (c) 22 (d) 130
  33. 33.Which term of the AP 10, 12, 14, 16, … is 62? (a) 27th (b) 28th (c) 26th (d) 31st
  34. 34.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 32 (b) 34 (c) 33 (d) 41
  35. 35.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 3906 (c) 1922 (d) 1891
  36. 36.What is the 10th term of the AP 12, 16, 20, 24, …? (a) 40 (b) 52 (c) 48 (d) 36
  37. 37.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 234 (b) 42 (c) 468 (d) 252
  38. 38.What is the 21st term of the AP 9, 12, 15, 18, …? (a) 60 (b) 72 (c) 69 (d) 63
  39. 39.What is the 33rd term of the AP 19, 23, 27, 31, …? (a) 147 (b) 128 (c) 132 (d) 151
  40. 40.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 9 (b) 42 (c) 43 (d) 84

Answer key

  1. 91
  2. 142
  3. 58
  4. 85
  5. 252
  6. 25
  7. 21
  8. 492
  9. 279
  10. 55
  11. 10th
  12. 576
  13. 100
  14. 16
  15. 171
  16. 29
  17. 324
  18. 184
  19. 66
  20. 36th
  21. 117
  22. 13th
  23. 19
  24. 278
  25. 111
  26. 70
  27. 43
  28. 91
  29. 50
  30. 86
  31. 42
  32. 130
  33. 27th
  34. 33
  35. 1953
  36. 48
  37. 234
  38. 69
  39. 147
  40. 42

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