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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 664 · 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 20th term of the AP 4, 6, 8, 10, …? (a) 42 (b) 44 (c) 40 (d) 38
  2. 2.Which term of the AP 2, 10, 18, 26, … is 138? (a) 20th (b) 17th (c) 18th (d) 19th
  3. 3.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 114 (b) 15 (c) 120 (d) 228
  4. 4.What is the missing term in the AP 18, 25, ?, 39, 46? (a) 33 (b) 39 (c) 31 (d) 32
  5. 5.What is the 12th term of the AP 18, 25, 32, 39, …? (a) 84 (b) 102 (c) 95 (d) 77
  6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 930 (c) 465 (d) 59
  7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 306 (d) 33
  8. 8.What is the 11th term of the AP 4, 12, 20, 28, …? (a) 80 (b) 88 (c) 92 (d) 84
  9. 9.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 13 (d) 28
  10. 10.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 2862 (c) 1432 (d) 1431
  11. 11.What is the missing term in the AP 15, 19, 23, ?, 31? (a) 28 (b) 27 (c) 26 (d) 31
  12. 12.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 190 (b) 210 (c) 380 (d) 37
  13. 13.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 4830 (c) 2416 (d) 2415
  14. 14.What is the 10th term of the AP 18, 25, 32, 39, …? (a) 70 (b) 63 (c) 88 (d) 81
  15. 15.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 4005 (c) 8190 (d) 4095
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 72 (d) 36
  17. 17.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4186 (c) 4187 (d) 8372
  18. 18.Which term of the AP 10, 18, 26, 34, … is 186? (a) 22nd (b) 24th (c) 23rd (d) 25th
  19. 19.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 242 (b) 121 (c) 16 (d) 122
  20. 20.What is the 27th term of the AP 12, 14, 16, 18, …? (a) 54 (b) 52 (c) 66 (d) 64
  21. 21.What is the 21st term of the AP 2, 4, 6, 8, …? (a) 40 (b) 43 (c) 42 (d) 44
  22. 22.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  23. 23.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1176 (c) 1226 (d) 1225
  24. 24.What is the 13th term of the AP 1, 10, 19, 28, …? (a) 108 (b) 109 (c) 118 (d) 117
  25. 25.What is the 27th term of the AP 9, 14, 19, 24, …? (a) 135 (b) 130 (c) 144 (d) 139
  26. 26.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 10 (b) 7 (c) 6 (d) 8
  27. 27.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 1953 (d) 2016
  28. 28.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 6642 (c) 3321 (d) 3240
  29. 29.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 28 (b) 216 (c) 108 (d) 120
  30. 30.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 23 (b) 26 (c) 21 (d) 22
  31. 31.Which term of the AP 4, 11, 18, 25, … is 193? (a) 27th (b) 29th (c) 28th (d) 30th
  32. 32.What is the 12th term of the AP 14, 18, 22, 26, …? (a) 44 (b) 62 (c) 58 (d) 48
  33. 33.What is the 12th term of the AP 10, 13, 16, 19, …? (a) 46 (b) 33 (c) 36 (d) 43
  34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 17 (d) 81
  35. 35.What is the 20th term of the AP 10, 17, 24, 31, …? (a) 150 (b) 140 (c) 133 (d) 143
  36. 36.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 35 (b) 30 (c) 29 (d) 31
  37. 37.Which term of the AP 10, 14, 18, 22, … is 134? (a) 34th (b) 33rd (c) 31st (d) 32nd
  38. 38.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 156 (d) 78
  39. 39.What is the 36th term of the AP 1, 7, 13, 19, …? (a) 217 (b) 216 (c) 210 (d) 211
  40. 40.Which term of the AP 3, 9, 15, 21, … is 165? (a) 28th (b) 27th (c) 30th (d) 29th

Answer key

  1. 42
  2. 18th
  3. 114
  4. 32
  5. 95
  6. 900
  7. 289
  8. 84
  9. 49
  10. 1431
  11. 27
  12. 190
  13. 2415
  14. 81
  15. 4095
  16. 64
  17. 4186
  18. 23rd
  19. 121
  20. 64
  21. 42
  22. 529
  23. 1225
  24. 109
  25. 139
  26. 7
  27. 2016
  28. 3321
  29. 108
  30. 22
  31. 28th
  32. 58
  33. 43
  34. 81
  35. 143
  36. 30
  37. 32nd
  38. 144
  39. 211
  40. 28th

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