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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 585 · 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 terms of the AP 2, 7, 12, …? (a) 65 (b) 22 (c) 120 (d) 60
  2. 2.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 312 (b) 37 (c) 156 (d) 176
  3. 3.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 35 (d) 342
  4. 4.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 245 (b) 270 (c) 47 (d) 490
  5. 5.What is the 34th term of the AP 18, 20, 22, 24, …? (a) 68 (b) 86 (c) 84 (d) 66
  6. 6.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 14 (b) 19 (c) 16 (d) 15
  7. 7.What is the 18th term of the AP 1, 10, 19, 28, …? (a) 162 (b) 154 (c) 163 (d) 153
  8. 8.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 30 (c) 140 (d) 126
  9. 9.What is the 18th term of the AP 3, 7, 11, 15, …? (a) 75 (b) 71 (c) 68 (d) 72
  10. 10.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 112 (b) 224 (c) 21 (d) 120
  11. 11.What is the 17th term of the AP 1, 8, 15, 22, …? (a) 119 (b) 112 (c) 120 (d) 113
  12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  13. 13.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 100 (b) 14 (c) 50 (d) 55
  14. 14.What is the 32nd term of the AP 18, 22, 26, 30, …? (a) 142 (b) 128 (c) 146 (d) 124
  15. 15.What is the 14th term of the AP 16, 19, 22, 25, …? (a) 39 (b) 58 (c) 55 (d) 42
  16. 16.Which term of the AP 11, 20, 29, 38, … is 272? (a) 29th (b) 32nd (c) 30th (d) 31st
  17. 17.What is the 40th term of the AP 15, 20, 25, 30, …? (a) 215 (b) 210 (c) 200 (d) 195
  18. 18.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 120 (b) 230 (c) 16 (d) 115
  19. 19.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 9 (b) 14 (c) 7 (d) 8
  20. 20.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
  21. 21.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 696 (b) 372 (c) 51 (d) 348
  22. 22.What is the 14th term of the AP 19, 24, 29, 34, …? (a) 70 (b) 65 (c) 84 (d) 89
  23. 23.What is the 10th term of the AP 16, 22, 28, 34, …? (a) 76 (b) 60 (c) 54 (d) 70
  24. 24.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 21 (b) 14 (c) 16 (d) 15
  25. 25.Which term of the AP 10, 19, 28, 37, … is 109? (a) 12th (b) 13th (c) 11th (d) 14th
  26. 26.What is the 34th term of the AP 16, 25, 34, 43, …? (a) 322 (b) 306 (c) 313 (d) 297
  27. 27.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 7 (b) 6 (c) 13 (d) 8
  28. 28.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3240 (c) 3321 (d) 3322
  29. 29.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 3741 (c) 3828 (d) 7656
  30. 30.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 15 (b) 13 (c) 14 (d) 12
  31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  32. 32.Which term of the AP 18, 20, 22, 24, … is 50? (a) 16th (b) 25th (c) 17th (d) 18th
  33. 33.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 73 (b) 144 (c) 72 (d) 12
  34. 34.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  35. 35.What is the missing term in the AP 6, 12, ?, 24, 30? (a) 24 (b) 19 (c) 17 (d) 18
  36. 36.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 36 (b) 40 (c) 72 (d) 8
  37. 37.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 4160 (c) 2016 (d) 2048
  38. 38.What is the 15th term of the AP 2, 9, 16, 23, …? (a) 107 (b) 105 (c) 98 (d) 100
  39. 39.Which term of the AP 15, 20, 25, 30, … is 145? (a) 26th (b) 29th (c) 28th (d) 27th
  40. 40.What is the 40th term of the AP 15, 24, 33, 42, …? (a) 351 (b) 366 (c) 360 (d) 375

Answer key

  1. 60
  2. 156
  3. 324
  4. 245
  5. 84
  6. 15
  7. 154
  8. 126
  9. 71
  10. 112
  11. 113
  12. 81
  13. 50
  14. 142
  15. 55
  16. 30th
  17. 210
  18. 115
  19. 8
  20. 676
  21. 348
  22. 84
  23. 70
  24. 15
  25. 12th
  26. 313
  27. 7
  28. 3321
  29. 3828
  30. 13
  31. 841
  32. 17th
  33. 72
  34. 625
  35. 18
  36. 36
  37. 2080
  38. 100
  39. 27th
  40. 366

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