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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 101 · 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 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 25 (d) 9
  2. 2.Which term of the AP 17, 23, 29, 35, … is 221? (a) 37th (b) 36th (c) 34th (d) 35th
  3. 3.What is the 24th term of the AP 9, 12, 15, 18, …? (a) 81 (b) 72 (c) 78 (d) 69
  4. 4.Which term of the AP 12, 15, 18, 21, … is 126? (a) 38th (b) 40th (c) 39th (d) 42nd
  5. 5.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 7482 (c) 3698 (d) 3741
  6. 6.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 27 (d) 105
  7. 7.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 306 (d) 154
  8. 8.What is the 26th term of the AP 13, 18, 23, 28, …? (a) 138 (b) 130 (c) 125 (d) 143
  9. 9.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 300 (b) 47 (c) 600 (d) 324
  10. 10.What is the 40th term of the AP 13, 22, 31, 40, …? (a) 351 (b) 364 (c) 360 (d) 373
  11. 11.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 88 (c) 18 (d) 176
  12. 12.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 116 (b) 232 (c) 128 (d) 25
  13. 13.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 240 (b) 130 (c) 120 (d) 21
  14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 153 (d) 289
  15. 15.What is the 30th term of the AP 1, 8, 15, 22, …? (a) 211 (b) 203 (c) 210 (d) 204
  16. 16.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 552 (c) 276 (d) 253
  17. 17.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 4692 (c) 2346 (d) 2312
  18. 18.What is the 11th term of the AP 2, 5, 8, 11, …? (a) 30 (b) 33 (c) 35 (d) 32
  19. 19.What is the missing term in the AP 16, 20, ?, 28, 32? (a) 23 (b) 25 (c) 24 (d) 28
  20. 20.What is the 29th term of the AP 10, 19, 28, 37, …? (a) 271 (b) 262 (c) 252 (d) 261
  21. 21.What is the 23rd term of the AP 13, 19, 25, 31, …? (a) 151 (b) 145 (c) 132 (d) 138
  22. 22.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 223 (b) 35 (c) 440 (d) 220
  23. 23.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 128 (b) 136 (c) 23 (d) 256
  24. 24.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 272 (c) 136 (d) 120
  25. 25.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 225 (d) 120
  26. 26.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 9 (b) 7 (c) 15 (d) 8
  27. 27.Which term of the AP 18, 21, 24, 27, … is 108? (a) 32nd (b) 36th (c) 31st (d) 30th
  28. 28.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4851 (c) 4951 (d) 9900
  29. 29.Which term of the AP 7, 11, 15, 19, … is 111? (a) 26th (b) 27th (c) 29th (d) 28th
  30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 121 (d) 132
  31. 31.What is the 28th term of the AP 15, 18, 21, 24, …? (a) 84 (b) 81 (c) 96 (d) 99
  32. 32.What is the 38th term of the AP 1, 10, 19, 28, …? (a) 343 (b) 342 (c) 334 (d) 333
  33. 33.What is the 28th term of the AP 7, 13, 19, 25, …? (a) 175 (b) 168 (c) 169 (d) 162
  34. 34.What is the 11th term of the AP 20, 26, 32, 38, …? (a) 80 (b) 66 (c) 60 (d) 86
  35. 35.What is the 17th term of the AP 13, 15, 17, 19, …? (a) 32 (b) 47 (c) 34 (d) 45
  36. 36.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 1892 (c) 946 (d) 947
  37. 37.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 5 (b) 7 (c) 3 (d) 4
  38. 38.Which term of the AP 4, 7, 10, 13, … is 82? (a) 29th (b) 27th (c) 26th (d) 28th
  39. 39.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 21 (b) 28 (c) 23 (d) 22
  40. 40.What is the 18th term of the AP 18, 27, 36, 45, …? (a) 153 (b) 162 (c) 171 (d) 180

Answer key

  1. 25
  2. 35th
  3. 78
  4. 39th
  5. 3741
  6. 196
  7. 153
  8. 138
  9. 300
  10. 364
  11. 88
  12. 116
  13. 120
  14. 289
  15. 204
  16. 276
  17. 2346
  18. 32
  19. 24
  20. 262
  21. 145
  22. 220
  23. 128
  24. 136
  25. 225
  26. 8
  27. 31st
  28. 4950
  29. 27th
  30. 121
  31. 96
  32. 334
  33. 169
  34. 80
  35. 45
  36. 946
  37. 4
  38. 27th
  39. 22
  40. 171

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