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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 450 · 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 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 35 (c) 10 (d) 30
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  3. 3.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 529 (d) 45
  4. 4.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 145 (b) 290 (c) 160 (d) 28
  5. 5.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 48 (b) 280 (c) 510 (d) 255
  6. 6.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 4950 (c) 5000 (d) 5050
  7. 7.What is the 29th term of the AP 6, 14, 22, 30, …? (a) 232 (b) 238 (c) 230 (d) 224
  8. 8.What is the 17th term of the AP 2, 5, 8, 11, …? (a) 48 (b) 53 (c) 50 (d) 51
  9. 9.What is the sum of all the whole numbers from 1 to 46? (a) 1081 (b) 1058 (c) 1035 (d) 2162
  10. 10.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 12 (c) 75 (d) 150
  11. 11.What is the 11th term of the AP 20, 28, 36, 44, …? (a) 100 (b) 88 (c) 108 (d) 80
  12. 12.Which term of the AP 5, 8, 11, 14, … is 83? (a) 29th (b) 26th (c) 28th (d) 27th
  13. 13.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 21 (b) 19 (c) 20 (d) 27
  14. 14.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 147 (b) 36 (c) 294 (d) 152
  15. 15.Which term of the AP 14, 22, 30, 38, … is 246? (a) 29th (b) 32nd (c) 30th (d) 31st
  16. 16.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 41 (b) 34 (c) 35 (d) 36
  17. 17.Which term of the AP 15, 19, 23, 27, … is 123? (a) 30th (b) 28th (c) 29th (d) 27th
  18. 18.What is the missing term in the AP 14, ?, 18, 20, 22? (a) 16 (b) 17 (c) 15 (d) 18
  19. 19.Which term of the AP 4, 12, 20, 28, … is 220? (a) 28th (b) 29th (c) 27th (d) 30th
  20. 20.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 392 (b) 217 (c) 46 (d) 196
  21. 21.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 16 (b) 19 (c) 14 (d) 15
  22. 22.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 333 (b) 612 (c) 306 (d) 58
  23. 23.Which term of the AP 6, 8, 10, 12, … is 42? (a) 21st (b) 20th (c) 18th (d) 19th
  24. 24.What is the 19th term of the AP 13, 20, 27, 34, …? (a) 126 (b) 146 (c) 139 (d) 133
  25. 25.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 26 (b) 96 (c) 108 (d) 192
  26. 26.Which term of the AP 2, 6, 10, 14, … is 106? (a) 27th (b) 26th (c) 29th (d) 28th
  27. 27.Which term of the AP 9, 13, 17, 21, … is 93? (a) 23rd (b) 24th (c) 21st (d) 22nd
  28. 28.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 26 (b) 28 (c) 27 (d) 35
  29. 29.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 102 (c) 120 (d) 204
  30. 30.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1771 (c) 1711 (d) 1770
  31. 31.What is the 36th term of the AP 14, 19, 24, 29, …? (a) 175 (b) 194 (c) 180 (d) 189
  32. 32.Which term of the AP 7, 15, 23, 31, … is 183? (a) 25th (b) 24th (c) 22nd (d) 23rd
  33. 33.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 253 (c) 43 (d) 484
  34. 34.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 23 (b) 27 (c) 21 (d) 22
  35. 35.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 21 (b) 20 (c) 19 (d) 23
  36. 36.What is the 32nd term of the AP 3, 11, 19, 27, …? (a) 259 (b) 248 (c) 251 (d) 256
  37. 37.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 154 (b) 266 (c) 37 (d) 133
  38. 38.What is the 14th term of the AP 11, 17, 23, 29, …? (a) 84 (b) 95 (c) 89 (d) 78
  39. 39.What is the 16th term of the AP 11, 15, 19, 23, …? (a) 71 (b) 75 (c) 60 (d) 64
  40. 40.Which term of the AP 14, 18, 22, 26, … is 158? (a) 38th (b) 37th (c) 36th (d) 39th

Answer key

  1. 30
  2. 64
  3. 529
  4. 145
  5. 255
  6. 5050
  7. 230
  8. 50
  9. 1081
  10. 75
  11. 100
  12. 27th
  13. 20
  14. 147
  15. 30th
  16. 35
  17. 28th
  18. 16
  19. 28th
  20. 196
  21. 15
  22. 306
  23. 19th
  24. 139
  25. 96
  26. 27th
  27. 22nd
  28. 27
  29. 102
  30. 1770
  31. 189
  32. 23rd
  33. 484
  34. 22
  35. 20
  36. 251
  37. 133
  38. 89
  39. 71
  40. 37th

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