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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 54 · 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 7, 14, 21, ?, 35? (a) 27 (b) 35 (c) 29 (d) 28
  2. 2.What is the 32nd term of the AP 19, 24, 29, 34, …? (a) 160 (b) 179 (c) 174 (d) 155
  3. 3.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 1640 (c) 820 (d) 780
  4. 4.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 308 (b) 19 (c) 155 (d) 154
  5. 5.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 272 (d) 136
  6. 6.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 125 (b) 110 (c) 220 (d) 34
  7. 7.What is the 22nd term of the AP 8, 15, 22, 29, …? (a) 155 (b) 154 (c) 162 (d) 147
  8. 8.What is the 26th term of the AP 6, 12, 18, 24, …? (a) 162 (b) 157 (c) 150 (d) 156
  9. 9.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  10. 10.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 27 (b) 28 (c) 34 (d) 29
  11. 11.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 220 (c) 20 (d) 110
  12. 12.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 15 (b) 17 (c) 14 (d) 13
  13. 13.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 72 (c) 73 (d) 12
  14. 14.Which term of the AP 16, 24, 32, 40, … is 72? (a) 8th (b) 7th (c) 10th (d) 9th
  15. 15.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 51 (d) 351
  16. 16.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 28 (b) 198 (c) 396 (d) 209
  17. 17.Which term of the AP 17, 19, 21, 23, … is 33? (a) 9th (b) 8th (c) 10th (d) 11th
  18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  19. 19.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 18 (b) 19 (c) 23 (d) 20
  20. 20.What is the 11th term of the AP 2, 5, 8, 11, …? (a) 30 (b) 33 (c) 32 (d) 35
  21. 21.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 94 (c) 22 (d) 182
  22. 22.What is the missing term in the AP 20, 25, 30, ?, 40? (a) 35 (b) 34 (c) 36 (d) 40
  23. 23.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 302 (b) 594 (c) 297 (d) 52
  24. 24.What is the 24th term of the AP 17, 26, 35, 44, …? (a) 216 (b) 207 (c) 233 (d) 224
  25. 25.What is the 25th term of the AP 16, 20, 24, 28, …? (a) 116 (b) 96 (c) 112 (d) 100
  26. 26.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 51 (c) 12 (d) 50
  27. 27.Which term of the AP 9, 18, 27, 36, … is 207? (a) 22nd (b) 23rd (c) 24th (d) 25th
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  29. 29.What is the 31st term of the AP 16, 25, 34, 43, …? (a) 295 (b) 270 (c) 286 (d) 279
  30. 30.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 26 (b) 24 (c) 25 (d) 30
  31. 31.What is the 14th term of the AP 2, 8, 14, 20, …? (a) 80 (b) 84 (c) 86 (d) 78
  32. 32.What is the 15th term of the AP 17, 21, 25, 29, …? (a) 60 (b) 77 (c) 56 (d) 73
  33. 33.What is the 16th term of the AP 4, 6, 8, 10, …? (a) 30 (b) 36 (c) 34 (d) 32
  34. 34.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 252 (b) 129 (c) 126 (d) 27
  35. 35.What is the 27th term of the AP 18, 20, 22, 24, …? (a) 54 (b) 70 (c) 52 (d) 72
  36. 36.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2850 (c) 2888 (d) 2926
  37. 37.What is the 10th term of the AP 5, 8, 11, 14, …? (a) 27 (b) 35 (c) 30 (d) 32
  38. 38.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 17 (c) 45 (d) 90
  39. 39.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 45 (b) 90 (c) 11 (d) 46
  40. 40.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 138 (b) 27 (c) 270 (d) 135

Answer key

  1. 28
  2. 174
  3. 820
  4. 154
  5. 256
  6. 110
  7. 155
  8. 156
  9. 289
  10. 28
  11. 110
  12. 14
  13. 72
  14. 8th
  15. 676
  16. 198
  17. 9th
  18. 529
  19. 19
  20. 32
  21. 91
  22. 35
  23. 297
  24. 224
  25. 112
  26. 50
  27. 23rd
  28. 100
  29. 286
  30. 25
  31. 80
  32. 73
  33. 34
  34. 126
  35. 70
  36. 2926
  37. 32
  38. 45
  39. 45
  40. 135

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