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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 260 · 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 9, ?, 15, 18, 21? (a) 12 (b) 13 (c) 15 (d) 11
  2. 2.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 276 (c) 552 (d) 277
  3. 3.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 53 (d) 729
  4. 4.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
  5. 5.What is the 37th term of the AP 10, 15, 20, 25, …? (a) 180 (b) 195 (c) 185 (d) 190
  6. 6.What is the 22nd term of the AP 18, 22, 26, 30, …? (a) 106 (b) 88 (c) 102 (d) 84
  7. 7.Which term of the AP 3, 11, 19, 27, … is 99? (a) 15th (b) 12th (c) 14th (d) 13th
  8. 8.What is the 35th term of the AP 6, 13, 20, 27, …? (a) 238 (b) 244 (c) 251 (d) 245
  9. 9.Which term of the AP 4, 12, 20, 28, … is 316? (a) 41st (b) 42nd (c) 39th (d) 40th
  10. 10.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 9900 (c) 4851 (d) 4950
  11. 11.What is the 25th term of the AP 12, 15, 18, 21, …? (a) 75 (b) 87 (c) 72 (d) 84
  12. 12.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 2628 (c) 2701 (d) 5402
  13. 13.Which term of the AP 2, 4, 6, 8, … is 38? (a) 21st (b) 19th (c) 18th (d) 20th
  14. 14.Which term of the AP 7, 12, 17, 22, … is 167? (a) 33rd (b) 32nd (c) 35th (d) 34th
  15. 15.What is the 37th term of the AP 5, 12, 19, 26, …? (a) 259 (b) 257 (c) 252 (d) 264
  16. 16.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4851 (c) 4753 (d) 4802
  17. 17.What is the 25th term of the AP 17, 20, 23, 26, …? (a) 89 (b) 75 (c) 72 (d) 92
  18. 18.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 15 (d) 36
  19. 19.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1226 (c) 1225 (d) 1176
  20. 20.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2016 (c) 1953 (d) 2017
  21. 21.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  22. 22.What is the 21st term of the AP 2, 4, 6, 8, …? (a) 42 (b) 43 (c) 44 (d) 40
  23. 23.Which term of the AP 6, 8, 10, 12, … is 60? (a) 30th (b) 27th (c) 28th (d) 29th
  24. 24.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 440 (b) 30 (c) 220 (d) 231
  25. 25.Which term of the AP 3, 9, 15, 21, … is 99? (a) 18th (b) 16th (c) 17th (d) 19th
  26. 26.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 11 (b) 10 (c) 9 (d) 18
  27. 27.What is the missing term in the AP 15, 19, ?, 27, 31? (a) 27 (b) 24 (c) 22 (d) 23
  28. 28.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 496 (b) 248 (c) 52 (d) 272
  29. 29.What is the 20th term of the AP 9, 14, 19, 24, …? (a) 109 (b) 100 (c) 104 (d) 95
  30. 30.What is the 26th term of the AP 7, 15, 23, 31, …? (a) 200 (b) 208 (c) 207 (d) 215
  31. 31.Which term of the AP 8, 16, 24, 32, … is 104? (a) 12th (b) 15th (c) 14th (d) 13th
  32. 32.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 192 (b) 96 (c) 108 (d) 26
  33. 33.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 120 (b) 15 (c) 228 (d) 114
  34. 34.Which term of the AP 6, 14, 22, 30, … is 254? (a) 32nd (b) 33rd (c) 31st (d) 34th
  35. 35.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2485 (c) 2557 (d) 2556
  36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 435 (d) 870
  37. 37.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 330 (c) 165 (d) 20
  38. 38.What is the 35th term of the AP 15, 20, 25, 30, …? (a) 190 (b) 185 (c) 175 (d) 170
  39. 39.Which term of the AP 6, 11, 16, 21, … is 166? (a) 35th (b) 32nd (c) 33rd (d) 34th
  40. 40.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 364 (b) 44 (c) 203 (d) 182

Answer key

  1. 12
  2. 276
  3. 729
  4. 169
  5. 190
  6. 102
  7. 13th
  8. 244
  9. 40th
  10. 4950
  11. 84
  12. 2701
  13. 19th
  14. 33rd
  15. 257
  16. 4851
  17. 89
  18. 64
  19. 1225
  20. 2016
  21. 529
  22. 42
  23. 28th
  24. 220
  25. 17th
  26. 10
  27. 23
  28. 248
  29. 104
  30. 207
  31. 13th
  32. 96
  33. 114
  34. 32nd
  35. 2556
  36. 841
  37. 165
  38. 185
  39. 33rd
  40. 182

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