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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 614 · 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 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  2. 2.What is the 16th term of the AP 18, 21, 24, 27, …? (a) 66 (b) 63 (c) 48 (d) 45
  3. 3.Which term of the AP 5, 10, 15, 20, … is 90? (a) 19th (b) 17th (c) 18th (d) 20th
  4. 4.What is the sum of the first 7 terms of the AP 10, 14, 18, …? (a) 34 (b) 168 (c) 308 (d) 154
  5. 5.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 15 (b) 10 (c) 9 (d) 8
  6. 6.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 22 (b) 92 (c) 104 (d) 184
  7. 7.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 7 (b) 11 (c) 5 (d) 6
  8. 8.Which term of the AP 3, 11, 19, 27, … is 147? (a) 20th (b) 18th (c) 21st (d) 19th
  9. 9.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 91 (b) 180 (c) 14 (d) 90
  10. 10.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 212 (b) 418 (c) 209 (d) 34
  11. 11.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 288 (b) 144 (c) 32 (d) 160
  12. 12.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 84 (b) 19 (c) 90 (d) 168
  13. 13.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 32 (b) 26 (c) 24 (d) 25
  14. 14.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 138 (c) 14 (d) 69
  15. 15.What is the 21st term of the AP 1, 5, 9, 13, …? (a) 80 (b) 84 (c) 81 (d) 85
  16. 16.What is the 32nd term of the AP 13, 17, 21, 25, …? (a) 141 (b) 137 (c) 124 (d) 128
  17. 17.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 50 (b) 100 (c) 14 (d) 55
  18. 18.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 30 (b) 31 (c) 32 (d) 38
  19. 19.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 14 (b) 95 (c) 100 (d) 190
  20. 20.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 300 (c) 150 (d) 160
  21. 21.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2279 (c) 2211 (d) 4556
  22. 22.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 23 (b) 18 (c) 17 (d) 19
  23. 23.Which term of the AP 17, 19, 21, 23, … is 73? (a) 28th (b) 29th (c) 31st (d) 30th
  24. 24.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 1482 (c) 741 (d) 703
  25. 25.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 25 (b) 27 (c) 33 (d) 26
  26. 26.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 19 (b) 110 (c) 200 (d) 100
  27. 27.What is the 34th term of the AP 16, 23, 30, 37, …? (a) 247 (b) 231 (c) 254 (d) 238
  28. 28.Which term of the AP 14, 22, 30, 38, … is 294? (a) 37th (b) 36th (c) 35th (d) 38th
  29. 29.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 8 (b) 14 (c) 9 (d) 7
  30. 30.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 162 (b) 288 (c) 39 (d) 144
  31. 31.What is the 18th term of the AP 11, 13, 15, 17, …? (a) 45 (b) 36 (c) 47 (d) 34
  32. 32.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 600 (b) 57 (c) 330 (d) 300
  33. 33.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 87 (b) 96 (c) 22 (d) 174
  34. 34.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 174 (b) 31 (c) 171 (d) 342
  35. 35.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 9 (b) 7 (c) 6 (d) 8
  36. 36.What is the 34th term of the AP 15, 20, 25, 30, …? (a) 165 (b) 180 (c) 185 (d) 170
  37. 37.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 129 (b) 126 (c) 26 (d) 252
  38. 38.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 13 (b) 12 (c) 10 (d) 11
  39. 39.What is the 23rd term of the AP 17, 23, 29, 35, …? (a) 138 (b) 155 (c) 149 (d) 132
  40. 40.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 253 (c) 276 (d) 552

Answer key

  1. 121
  2. 63
  3. 18th
  4. 154
  5. 9
  6. 92
  7. 6
  8. 19th
  9. 90
  10. 209
  11. 144
  12. 84
  13. 25
  14. 69
  15. 81
  16. 137
  17. 50
  18. 31
  19. 95
  20. 150
  21. 2278
  22. 18
  23. 29th
  24. 741
  25. 26
  26. 100
  27. 247
  28. 36th
  29. 8
  30. 144
  31. 45
  32. 300
  33. 87
  34. 171
  35. 7
  36. 180
  37. 126
  38. 11
  39. 149
  40. 276

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