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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 520 · 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 14, 18, ?, 26, 30? (a) 26 (b) 23 (c) 21 (d) 22
  2. 2.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 348 (b) 174 (c) 20 (d) 180
  3. 3.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 130 (b) 25 (c) 65 (d) 80
  4. 4.Which term of the AP 10, 17, 24, 31, … is 164? (a) 22nd (b) 23rd (c) 24th (d) 25th
  5. 5.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 92 (c) 104 (d) 22
  6. 6.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 240 (b) 216 (c) 432 (d) 48
  7. 7.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 230 (b) 460 (c) 250 (d) 41
  8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
  9. 9.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 29 (c) 216 (d) 228
  10. 10.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100
  11. 11.What is the 39th term of the AP 13, 17, 21, 25, …? (a) 152 (b) 165 (c) 156 (d) 169
  12. 12.What is the 38th term of the AP 8, 17, 26, 35, …? (a) 341 (b) 350 (c) 342 (d) 333
  13. 13.Which term of the AP 15, 22, 29, 36, … is 253? (a) 36th (b) 34th (c) 37th (d) 35th
  14. 14.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 448 (b) 248 (c) 49 (d) 224
  15. 15.Which term of the AP 3, 5, 7, 9, … is 39? (a) 18th (b) 20th (c) 19th (d) 21st
  16. 16.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 12 (b) 10 (c) 11 (d) 9
  17. 17.What is the 33rd term of the AP 1, 3, 5, 7, …? (a) 66 (b) 65 (c) 64 (d) 67
  18. 18.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 19 (b) 16 (c) 15 (d) 17
  19. 19.Which term of the AP 12, 14, 16, 18, … is 68? (a) 34th (b) 29th (c) 30th (d) 28th
  20. 20.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 13 (b) 23 (c) 14 (d) 15
  21. 21.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  22. 22.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 91 (d) 182
  23. 23.Which term of the AP 1, 5, 9, 13, … is 105? (a) 26th (b) 29th (c) 28th (d) 27th
  24. 24.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 70 (c) 8 (d) 35
  25. 25.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 112 (b) 126 (c) 28 (d) 224
  26. 26.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 34 (b) 32 (c) 33 (d) 42
  27. 27.What is the 10th term of the AP 4, 9, 14, 19, …? (a) 49 (b) 45 (c) 50 (d) 54
  28. 28.What is the 25th term of the AP 20, 29, 38, 47, …? (a) 216 (b) 236 (c) 245 (d) 225
  29. 29.Which term of the AP 1, 9, 17, 25, … is 169? (a) 21st (b) 22nd (c) 24th (d) 23rd
  30. 30.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 30 (b) 256 (c) 144 (d) 128
  31. 31.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 231 (c) 232 (d) 462
  32. 32.What is the 14th term of the AP 20, 23, 26, 29, …? (a) 59 (b) 39 (c) 62 (d) 42
  33. 33.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 75 (c) 70 (d) 140
  34. 34.Which term of the AP 11, 19, 27, 35, … is 291? (a) 37th (b) 38th (c) 36th (d) 35th
  35. 35.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 66 (d) 156
  36. 36.What is the 22nd term of the AP 15, 19, 23, 27, …? (a) 99 (b) 84 (c) 88 (d) 103
  37. 37.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 84 (b) 17 (c) 154 (d) 77
  38. 38.What is the 23rd term of the AP 3, 12, 21, 30, …? (a) 210 (b) 207 (c) 201 (d) 198
  39. 39.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 27 (b) 170 (c) 85 (d) 90
  40. 40.What is the 18th term of the AP 9, 18, 27, 36, …? (a) 153 (b) 163 (c) 162 (d) 171

Answer key

  1. 22
  2. 174
  3. 65
  4. 23rd
  5. 92
  6. 216
  7. 230
  8. 529
  9. 216
  10. 100
  11. 165
  12. 341
  13. 35th
  14. 224
  15. 19th
  16. 10
  17. 65
  18. 16
  19. 29th
  20. 14
  21. 49
  22. 169
  23. 27th
  24. 35
  25. 112
  26. 33
  27. 49
  28. 236
  29. 22nd
  30. 128
  31. 231
  32. 59
  33. 70
  34. 36th
  35. 78
  36. 99
  37. 77
  38. 201
  39. 85
  40. 162

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