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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 165 · 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.Which term of the AP 6, 11, 16, 21, … is 96? (a) 19th (b) 20th (c) 21st (d) 18th
  2. 2.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 19 (b) 17 (c) 18 (d) 21
  3. 3.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 18 (b) 20 (c) 19 (d) 27
  4. 4.What is the 11th term of the AP 12, 16, 20, 24, …? (a) 52 (b) 40 (c) 44 (d) 56
  5. 5.What is the 11th term of the AP 2, 11, 20, 29, …? (a) 92 (b) 101 (c) 90 (d) 99
  6. 6.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 191 (c) 190 (d) 380
  7. 7.What is the 30th term of the AP 11, 14, 17, 20, …? (a) 87 (b) 90 (c) 101 (d) 98
  8. 8.Which term of the AP 11, 19, 27, 35, … is 163? (a) 21st (b) 22nd (c) 19th (d) 20th
  9. 9.Which term of the AP 4, 10, 16, 22, … is 64? (a) 12th (b) 11th (c) 10th (d) 13th
  10. 10.Which term of the AP 18, 21, 24, 27, … is 132? (a) 44th (b) 38th (c) 40th (d) 39th
  11. 11.What is the 26th term of the AP 4, 6, 8, 10, …? (a) 52 (b) 54 (c) 50 (d) 56
  12. 12.What is the 21st term of the AP 8, 16, 24, 32, …? (a) 160 (b) 176 (c) 169 (d) 168
  13. 13.What is the 13th term of the AP 14, 22, 30, 38, …? (a) 96 (b) 118 (c) 104 (d) 110
  14. 14.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 19 (b) 20 (c) 21 (d) 23
  15. 15.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 114 (b) 228 (c) 120 (d) 15
  16. 16.Which term of the AP 20, 23, 26, 29, … is 116? (a) 34th (b) 33rd (c) 32nd (d) 35th
  17. 17.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 100 (b) 200 (c) 30 (d) 105
  18. 18.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1225 (c) 1226 (d) 1176
  19. 19.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2450 (d) 2485
  20. 20.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 223 (b) 35 (c) 440 (d) 220
  21. 21.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 351 (c) 338 (d) 325
  22. 22.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 12 (b) 57 (c) 60 (d) 114
  23. 23.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 300 (c) 600 (d) 330
  24. 24.Which term of the AP 20, 23, 26, 29, … is 83? (a) 21st (b) 24th (c) 23rd (d) 22nd
  25. 25.Which term of the AP 17, 25, 33, 41, … is 225? (a) 28th (b) 26th (c) 29th (d) 27th
  26. 26.What is the 14th term of the AP 5, 7, 9, 11, …? (a) 26 (b) 28 (c) 31 (d) 33
  27. 27.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 112 (b) 21 (c) 210 (d) 105
  28. 28.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 3782 (c) 1891 (d) 1830
  29. 29.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 2352 (c) 1152 (d) 1176
  30. 30.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 128 (b) 256 (c) 23 (d) 136
  31. 31.Which term of the AP 15, 23, 31, 39, … is 271? (a) 32nd (b) 33rd (c) 35th (d) 34th
  32. 32.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 361 (d) 380
  33. 33.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 57 (b) 357 (c) 704 (d) 352
  34. 34.What is the 25th term of the AP 12, 18, 24, 30, …? (a) 144 (b) 150 (c) 162 (d) 156
  35. 35.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 350 (b) 196 (c) 175 (d) 43
  36. 36.What is the 34th term of the AP 11, 13, 15, 17, …? (a) 66 (b) 68 (c) 77 (d) 79
  37. 37.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1568 (c) 1540 (d) 1596
  38. 38.What is the 19th term of the AP 7, 9, 11, 13, …? (a) 38 (b) 36 (c) 45 (d) 43
  39. 39.What is the 18th term of the AP 11, 20, 29, 38, …? (a) 153 (b) 162 (c) 164 (d) 173
  40. 40.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 20 (c) 348 (d) 174

Answer key

  1. 19th
  2. 18
  3. 19
  4. 52
  5. 92
  6. 190
  7. 98
  8. 20th
  9. 11th
  10. 39th
  11. 54
  12. 168
  13. 110
  14. 20
  15. 114
  16. 33rd
  17. 100
  18. 1225
  19. 2485
  20. 220
  21. 351
  22. 57
  23. 300
  24. 22nd
  25. 27th
  26. 31
  27. 105
  28. 1891
  29. 1176
  30. 128
  31. 33rd
  32. 361
  33. 352
  34. 156
  35. 175
  36. 77
  37. 1596
  38. 43
  39. 164
  40. 174

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