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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 655 · 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 9 terms of the AP 2, 4, 6, …? (a) 180 (b) 99 (c) 90 (d) 18
  2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 49 (d) 650
  3. 3.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 41 (b) 10 (c) 80 (d) 40
  4. 4.What is the 19th term of the AP 2, 4, 6, 8, …? (a) 36 (b) 39 (c) 38 (d) 40
  5. 5.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 55 (d) 110
  6. 6.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 480 (b) 240 (c) 42 (d) 260
  7. 7.What is the missing term in the AP 9, 16, 23, ?, 37? (a) 31 (b) 37 (c) 29 (d) 30
  8. 8.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 105 (d) 27
  9. 9.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3403 (c) 6972 (d) 3486
  10. 10.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4371 (c) 4418 (d) 4465
  11. 11.What is the 36th term of the AP 9, 16, 23, 30, …? (a) 254 (b) 245 (c) 252 (d) 261
  12. 12.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 34 (b) 162 (c) 324 (d) 180
  13. 13.What is the missing term in the AP 9, ?, 19, 24, 29? (a) 15 (b) 13 (c) 14 (d) 19
  14. 14.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 72 (b) 936 (c) 468 (d) 504
  15. 15.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 372 (b) 56 (c) 342 (d) 684
  16. 16.What is the 21st term of the AP 3, 9, 15, 21, …? (a) 120 (b) 126 (c) 123 (d) 129
  17. 17.Which term of the AP 9, 12, 15, 18, … is 114? (a) 35th (b) 37th (c) 38th (d) 36th
  18. 18.Which term of the AP 6, 12, 18, 24, … is 174? (a) 30th (b) 29th (c) 28th (d) 31st
  19. 19.What is the 38th term of the AP 11, 14, 17, 20, …? (a) 111 (b) 122 (c) 125 (d) 114
  20. 20.What is the 14th term of the AP 12, 18, 24, 30, …? (a) 96 (b) 84 (c) 78 (d) 90
  21. 21.What is the 40th term of the AP 2, 8, 14, 20, …? (a) 240 (b) 242 (c) 236 (d) 234
  22. 22.What is the 16th term of the AP 19, 26, 33, 40, …? (a) 131 (b) 124 (c) 112 (d) 105
  23. 23.What is the missing term in the AP 14, 20, ?, 32, 38? (a) 26 (b) 27 (c) 25 (d) 32
  24. 24.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 132 (b) 11 (c) 67 (d) 66
  25. 25.Which term of the AP 14, 23, 32, 41, … is 248? (a) 29th (b) 26th (c) 28th (d) 27th
  26. 26.What is the 12th term of the AP 15, 24, 33, 42, …? (a) 108 (b) 123 (c) 99 (d) 114
  27. 27.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 435 (c) 465 (d) 930
  28. 28.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 21 (b) 24 (c) 22 (d) 20
  29. 29.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 156 (d) 78
  30. 30.What is the 17th term of the AP 1, 5, 9, 13, …? (a) 68 (b) 65 (c) 64 (d) 69
  31. 31.What is the 38th term of the AP 6, 14, 22, 30, …? (a) 304 (b) 296 (c) 302 (d) 310
  32. 32.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 25 (b) 24 (c) 26 (d) 29
  33. 33.What is the missing term in the AP 12, ?, 16, 18, 20? (a) 13 (b) 14 (c) 16 (d) 15
  34. 34.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  35. 35.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 50 (b) 55 (c) 14 (d) 100
  36. 36.What is the 25th term of the AP 13, 22, 31, 40, …? (a) 238 (b) 216 (c) 229 (d) 225
  37. 37.What is the 19th term of the AP 19, 27, 35, 43, …? (a) 163 (b) 144 (c) 152 (d) 171
  38. 38.What is the 11th term of the AP 16, 20, 24, 28, …? (a) 44 (b) 40 (c) 56 (d) 60
  39. 39.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 100 (b) 50 (c) 60 (d) 18
  40. 40.What is the 22nd term of the AP 17, 19, 21, 23, …? (a) 42 (b) 61 (c) 44 (d) 59

Answer key

  1. 90
  2. 625
  3. 40
  4. 38
  5. 55
  6. 240
  7. 30
  8. 196
  9. 3486
  10. 4465
  11. 254
  12. 162
  13. 14
  14. 468
  15. 342
  16. 123
  17. 36th
  18. 29th
  19. 122
  20. 90
  21. 236
  22. 124
  23. 26
  24. 66
  25. 27th
  26. 114
  27. 465
  28. 21
  29. 78
  30. 65
  31. 302
  32. 25
  33. 14
  34. 225
  35. 50
  36. 229
  37. 163
  38. 56
  39. 50
  40. 59

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