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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 198 · 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 6, ?, 20, 27, 34? (a) 13 (b) 20 (c) 12 (d) 14
  2. 2.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 140 (b) 280 (c) 154 (d) 32
  3. 3.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4851 (c) 4951 (d) 4950
  4. 4.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 264 (b) 246 (c) 492 (d) 37
  5. 5.What is the 15th term of the AP 11, 14, 17, 20, …? (a) 45 (b) 42 (c) 53 (d) 56
  6. 6.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 351 (c) 51 (d) 702
  7. 7.What is the 15th term of the AP 11, 17, 23, 29, …? (a) 101 (b) 95 (c) 90 (d) 84
  8. 8.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 27 (d) 210
  9. 9.What is the missing term in the AP 10, 17, ?, 31, 38? (a) 31 (b) 25 (c) 24 (d) 23
  10. 10.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 144 (b) 78 (c) 72 (d) 17
  11. 11.Which term of the AP 5, 10, 15, 20, … is 110? (a) 23rd (b) 24th (c) 21st (d) 22nd
  12. 12.Which term of the AP 9, 14, 19, 24, … is 54? (a) 10th (b) 11th (c) 12th (d) 9th
  13. 13.What is the 27th term of the AP 11, 19, 27, 35, …? (a) 219 (b) 227 (c) 208 (d) 216
  14. 14.Which term of the AP 6, 8, 10, 12, … is 72? (a) 34th (b) 36th (c) 35th (d) 33rd
  15. 15.Which term of the AP 16, 21, 26, 31, … is 51? (a) 9th (b) 7th (c) 8th (d) 10th
  16. 16.Which term of the AP 18, 24, 30, 36, … is 72? (a) 12th (b) 9th (c) 11th (d) 10th
  17. 17.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 272 (c) 136 (d) 120
  18. 18.What is the 38th term of the AP 4, 7, 10, 13, …? (a) 115 (b) 114 (c) 118 (d) 111
  19. 19.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 12 (b) 40 (c) 45 (d) 80
  20. 20.Which term of the AP 1, 10, 19, 28, … is 163? (a) 21st (b) 18th (c) 19th (d) 20th
  21. 21.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 136 (d) 31
  22. 22.What is the 12th term of the AP 4, 10, 16, 22, …? (a) 70 (b) 72 (c) 66 (d) 76
  23. 23.What is the 21st term of the AP 16, 24, 32, 40, …? (a) 176 (b) 160 (c) 184 (d) 168
  24. 24.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 35 (c) 8 (d) 36
  25. 25.What is the 13th term of the AP 20, 27, 34, 41, …? (a) 84 (b) 111 (c) 91 (d) 104
  26. 26.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 35 (b) 9 (c) 36 (d) 70
  27. 27.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 150 (b) 25 (c) 80 (d) 75
  28. 28.Which term of the AP 12, 19, 26, 33, … is 68? (a) 10th (b) 11th (c) 8th (d) 9th
  29. 29.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 360 (b) 198 (c) 180 (d) 36
  30. 30.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 26 (b) 22 (c) 21 (d) 23
  31. 31.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 16 (b) 126 (c) 132 (d) 252
  32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  33. 33.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 198 (b) 29 (c) 114 (d) 99
  34. 34.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 384 (b) 57 (c) 708 (d) 354
  35. 35.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 300 (d) 325
  36. 36.What is the 14th term of the AP 12, 16, 20, 24, …? (a) 52 (b) 56 (c) 68 (d) 64
  37. 37.What is the missing term in the AP 14, 19, 24, ?, 34? (a) 34 (b) 29 (c) 30 (d) 28
  38. 38.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 297 (b) 270 (c) 54 (d) 540
  39. 39.Which term of the AP 4, 6, 8, 10, … is 66? (a) 32nd (b) 33rd (c) 31st (d) 34th
  40. 40.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 6006 (c) 3004 (d) 2926

Answer key

  1. 13
  2. 140
  3. 4950
  4. 246
  5. 53
  6. 676
  7. 95
  8. 196
  9. 24
  10. 72
  11. 22nd
  12. 10th
  13. 219
  14. 34th
  15. 8th
  16. 10th
  17. 136
  18. 115
  19. 40
  20. 19th
  21. 256
  22. 70
  23. 176
  24. 35
  25. 104
  26. 35
  27. 75
  28. 9th
  29. 180
  30. 22
  31. 126
  32. 121
  33. 99
  34. 354
  35. 325
  36. 64
  37. 29
  38. 270
  39. 32nd
  40. 3003

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