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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 745 · 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 31st term of the AP 13, 21, 29, 37, …? (a) 261 (b) 248 (c) 240 (d) 253
  2. 2.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 25 (b) 80 (c) 65 (d) 130
  3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  4. 4.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 363 (b) 726 (c) 63 (d) 396
  5. 5.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 20 (b) 15 (c) 16 (d) 14
  6. 6.What is the 28th term of the AP 3, 9, 15, 21, …? (a) 162 (b) 168 (c) 171 (d) 165
  7. 7.What is the 26th term of the AP 8, 15, 22, 29, …? (a) 182 (b) 190 (c) 175 (d) 183
  8. 8.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 36 (c) 11 (d) 42
  9. 9.Which term of the AP 10, 17, 24, 31, … is 157? (a) 23rd (b) 22nd (c) 21st (d) 24th
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 351 (d) 51
  11. 11.What is the 35th term of the AP 12, 14, 16, 18, …? (a) 70 (b) 80 (c) 82 (d) 68
  12. 12.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 39 (b) 31 (c) 29 (d) 30
  13. 13.What is the 21st term of the AP 20, 23, 26, 29, …? (a) 63 (b) 83 (c) 80 (d) 60
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  15. 15.Which term of the AP 16, 21, 26, 31, … is 211? (a) 40th (b) 42nd (c) 41st (d) 39th
  16. 16.What is the 18th term of the AP 10, 14, 18, 22, …? (a) 72 (b) 78 (c) 68 (d) 82
  17. 17.Which term of the AP 19, 27, 35, 43, … is 331? (a) 42nd (b) 39th (c) 40th (d) 41st
  18. 18.What is the 24th term of the AP 19, 24, 29, 34, …? (a) 134 (b) 139 (c) 115 (d) 120
  19. 19.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 171 (b) 35 (c) 189 (d) 342
  20. 20.What is the 24th term of the AP 1, 10, 19, 28, …? (a) 208 (b) 216 (c) 207 (d) 217
  21. 21.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 17 (b) 16 (c) 18 (d) 24
  22. 22.What is the 32nd term of the AP 6, 10, 14, 18, …? (a) 128 (b) 124 (c) 134 (d) 130
  23. 23.What is the 14th term of the AP 7, 12, 17, 22, …? (a) 77 (b) 65 (c) 72 (d) 70
  24. 24.Which term of the AP 4, 12, 20, 28, … is 76? (a) 9th (b) 10th (c) 11th (d) 12th
  25. 25.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 38 (b) 31 (c) 30 (d) 32
  26. 26.Which term of the AP 14, 18, 22, 26, … is 58? (a) 11th (b) 12th (c) 13th (d) 14th
  27. 27.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 497 (c) 465 (d) 496
  28. 28.What is the 40th term of the AP 2, 11, 20, 29, …? (a) 360 (b) 362 (c) 353 (d) 351
  29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 400 (d) 210
  30. 30.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 93 (b) 28 (c) 186 (d) 108
  31. 31.What is the 33rd term of the AP 8, 14, 20, 26, …? (a) 206 (b) 192 (c) 198 (d) 200
  32. 32.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 9 (b) 10 (c) 19 (d) 11
  33. 33.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 18 (b) 84 (c) 78 (d) 156
  34. 34.What is the 10th term of the AP 17, 26, 35, 44, …? (a) 81 (b) 107 (c) 90 (d) 98
  35. 35.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 12 (b) 150 (c) 80 (d) 75
  36. 36.What is the sum of all the whole numbers from 1 to 84? (a) 3570 (b) 7140 (c) 3528 (d) 3486
  37. 37.What is the 38th term of the AP 8, 10, 12, 14, …? (a) 84 (b) 74 (c) 82 (d) 76
  38. 38.What is the 18th term of the AP 19, 24, 29, 34, …? (a) 90 (b) 109 (c) 85 (d) 104
  39. 39.What is the 16th term of the AP 16, 20, 24, 28, …? (a) 64 (b) 76 (c) 60 (d) 80
  40. 40.What is the 16th term of the AP 12, 14, 16, 18, …? (a) 42 (b) 32 (c) 44 (d) 30

Answer key

  1. 253
  2. 65
  3. 361
  4. 363
  5. 15
  6. 165
  7. 183
  8. 36
  9. 22nd
  10. 676
  11. 80
  12. 30
  13. 80
  14. 121
  15. 40th
  16. 78
  17. 40th
  18. 134
  19. 171
  20. 208
  21. 17
  22. 130
  23. 72
  24. 10th
  25. 31
  26. 12th
  27. 496
  28. 353
  29. 400
  30. 93
  31. 200
  32. 10
  33. 78
  34. 98
  35. 75
  36. 3570
  37. 82
  38. 104
  39. 76
  40. 42

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