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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 575 · 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 2, ?, 10, 14, 18? (a) 7 (b) 10 (c) 6 (d) 5
  2. 2.What is the 24th term of the AP 15, 23, 31, 39, …? (a) 207 (b) 184 (c) 199 (d) 192
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  4. 4.What is the 36th term of the AP 9, 13, 17, 21, …? (a) 149 (b) 140 (c) 144 (d) 153
  5. 5.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 300 (c) 160 (d) 150
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  7. 7.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 22 (b) 20 (c) 21 (d) 27
  8. 8.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 192 (b) 189 (c) 33 (d) 378
  9. 9.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 16 (b) 15 (c) 22 (d) 14
  10. 10.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 48 (b) 44 (c) 88 (d) 9
  11. 11.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 12 (b) 15 (c) 11 (d) 10
  12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 182 (d) 169
  13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  14. 14.Which term of the AP 10, 15, 20, 25, … is 45? (a) 7th (b) 9th (c) 10th (d) 8th
  15. 15.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 38 (b) 384 (c) 192 (d) 208
  16. 16.Which term of the AP 6, 8, 10, 12, … is 80? (a) 39th (b) 37th (c) 38th (d) 40th
  17. 17.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 35 (d) 171
  18. 18.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 630 (d) 595
  19. 19.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 200 (b) 100 (c) 16 (d) 104
  20. 20.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 31 (b) 22 (c) 23 (d) 24
  21. 21.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 22 (b) 29 (c) 20 (d) 21
  22. 22.What is the 16th term of the AP 10, 14, 18, 22, …? (a) 60 (b) 70 (c) 64 (d) 74
  23. 23.What is the 35th term of the AP 18, 22, 26, 30, …? (a) 158 (b) 136 (c) 154 (d) 140
  24. 24.Which term of the AP 10, 19, 28, 37, … is 109? (a) 12th (b) 14th (c) 11th (d) 13th
  25. 25.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  26. 26.What is the 29th term of the AP 12, 16, 20, 24, …? (a) 112 (b) 116 (c) 124 (d) 128
  27. 27.Which term of the AP 20, 23, 26, 29, … is 101? (a) 27th (b) 30th (c) 29th (d) 28th
  28. 28.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 9506 (c) 4754 (d) 4753
  29. 29.Which term of the AP 7, 13, 19, 25, … is 97? (a) 18th (b) 17th (c) 15th (d) 16th
  30. 30.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 100 (b) 19 (c) 200 (d) 110
  31. 31.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2016 (c) 1953 (d) 2017
  32. 32.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 234 (b) 40 (c) 432 (d) 216
  33. 33.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 5 (b) 7 (c) 11 (d) 6
  34. 34.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 1035 (c) 1036 (d) 990
  35. 35.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 450 (b) 252 (c) 225 (d) 49
  36. 36.What is the missing term in the AP 11, ?, 27, 35, 43? (a) 18 (b) 19 (c) 27 (d) 20
  37. 37.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 27 (b) 22 (c) 21 (d) 20
  38. 38.Which term of the AP 11, 17, 23, 29, … is 155? (a) 26th (b) 25th (c) 24th (d) 27th
  39. 39.Which term of the AP 5, 11, 17, 23, … is 71? (a) 11th (b) 13th (c) 12th (d) 14th
  40. 40.What is the 37th term of the AP 20, 25, 30, 35, …? (a) 185 (b) 180 (c) 200 (d) 205

Answer key

  1. 6
  2. 199
  3. 225
  4. 149
  5. 150
  6. 289
  7. 21
  8. 189
  9. 15
  10. 44
  11. 11
  12. 169
  13. 121
  14. 8th
  15. 192
  16. 38th
  17. 324
  18. 630
  19. 100
  20. 23
  21. 21
  22. 70
  23. 154
  24. 12th
  25. 256
  26. 124
  27. 28th
  28. 4753
  29. 16th
  30. 100
  31. 2016
  32. 216
  33. 6
  34. 1035
  35. 225
  36. 19
  37. 21
  38. 25th
  39. 12th
  40. 200

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