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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 528 · 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.Which term of the AP 4, 7, 10, 13, … is 31? (a) 12th (b) 11th (c) 9th (d) 10th
  2. 2.What is the 14th term of the AP 8, 14, 20, 26, …? (a) 92 (b) 78 (c) 86 (d) 84
  3. 3.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 12 (b) 14 (c) 19 (d) 13
  4. 4.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 35 (c) 171 (d) 189
  5. 5.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 35 (d) 324
  6. 6.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 36 (b) 33 (c) 8 (d) 66
  7. 7.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 6642 (c) 3322 (d) 3240
  8. 8.What is the 19th term of the AP 1, 8, 15, 22, …? (a) 134 (b) 126 (c) 133 (d) 127
  9. 9.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 210 (b) 24 (c) 108 (d) 105
  10. 10.What is the 35th term of the AP 3, 7, 11, 15, …? (a) 143 (b) 140 (c) 136 (d) 139
  11. 11.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 352 (b) 192 (c) 36 (d) 176
  12. 12.Which term of the AP 4, 10, 16, 22, … is 142? (a) 25th (b) 24th (c) 26th (d) 23rd
  13. 13.What is the 10th term of the AP 1, 4, 7, 10, …? (a) 28 (b) 30 (c) 31 (d) 27
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 930 (d) 465
  15. 15.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  16. 16.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 326 (c) 325 (d) 300
  17. 17.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 91 (c) 182 (d) 78
  18. 18.What is the 24th term of the AP 3, 7, 11, 15, …? (a) 92 (b) 96 (c) 99 (d) 95
  19. 19.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 12 (b) 78 (c) 154 (d) 77
  20. 20.What is the 25th term of the AP 14, 17, 20, 23, …? (a) 72 (b) 89 (c) 75 (d) 86
  21. 21.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 203 (b) 396 (c) 198 (d) 42
  22. 22.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 27 (b) 114 (c) 204 (d) 102
  23. 23.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 91 (d) 169
  24. 24.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 38 (b) 140 (c) 161 (d) 280
  25. 25.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 37 (b) 46 (c) 38 (d) 39
  26. 26.What is the 34th term of the AP 4, 13, 22, 31, …? (a) 310 (b) 297 (c) 301 (d) 306
  27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 36 (d) 21
  28. 28.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 144 (b) 252 (c) 126 (d) 36
  29. 29.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 38 (b) 34 (c) 32 (d) 33
  30. 30.Which term of the AP 2, 10, 18, 26, … is 202? (a) 25th (b) 28th (c) 26th (d) 27th
  31. 31.Which term of the AP 13, 16, 19, 22, … is 46? (a) 14th (b) 13th (c) 12th (d) 11th
  32. 32.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 126 (b) 18 (c) 63 (d) 72
  33. 33.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 25 (b) 32 (c) 23 (d) 24
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 9 (d) 25
  35. 35.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4754 (c) 4656 (d) 9506
  36. 36.What is the 11th term of the AP 10, 16, 22, 28, …? (a) 60 (b) 76 (c) 66 (d) 70
  37. 37.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 231 (c) 232 (d) 462
  38. 38.What is the 36th term of the AP 13, 20, 27, 34, …? (a) 258 (b) 252 (c) 245 (d) 265
  39. 39.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 9 (c) 36 (d) 35
  40. 40.Which term of the AP 3, 6, 9, 12, … is 45? (a) 15th (b) 14th (c) 17th (d) 16th

Answer key

  1. 10th
  2. 86
  3. 13
  4. 171
  5. 324
  6. 33
  7. 3321
  8. 127
  9. 105
  10. 139
  11. 176
  12. 24th
  13. 28
  14. 900
  15. 441
  16. 325
  17. 91
  18. 95
  19. 77
  20. 86
  21. 198
  22. 102
  23. 169
  24. 140
  25. 38
  26. 301
  27. 36
  28. 126
  29. 33
  30. 26th
  31. 12th
  32. 63
  33. 24
  34. 25
  35. 4753
  36. 70
  37. 231
  38. 258
  39. 35
  40. 15th

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