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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 595 · 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 all the whole numbers from 1 to 46? (a) 1035 (b) 1081 (c) 1058 (d) 2162
  2. 2.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
  3. 3.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 72 (d) 36
  4. 4.What is the 17th term of the AP 4, 12, 20, 28, …? (a) 136 (b) 132 (c) 140 (d) 128
  5. 5.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 23 (b) 29 (c) 22 (d) 24
  6. 6.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 40 (b) 300 (c) 282 (d) 564
  7. 7.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 9506 (c) 4754 (d) 4656
  8. 8.What is the 23rd term of the AP 6, 10, 14, 18, …? (a) 92 (b) 98 (c) 88 (d) 94
  9. 9.What is the 28th term of the AP 7, 10, 13, 16, …? (a) 84 (b) 91 (c) 81 (d) 88
  10. 10.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 33 (b) 246 (c) 123 (d) 138
  11. 11.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 256 (b) 128 (c) 136 (d) 23
  12. 12.What is the missing term in the AP 12, 19, 26, ?, 40? (a) 32 (b) 40 (c) 33 (d) 34
  13. 13.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 110 (c) 50 (d) 55
  14. 14.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 19 (b) 15 (c) 16 (d) 17
  15. 15.Which term of the AP 18, 26, 34, 42, … is 218? (a) 27th (b) 28th (c) 26th (d) 25th
  16. 16.Which term of the AP 3, 11, 19, 27, … is 163? (a) 22nd (b) 20th (c) 21st (d) 23rd
  17. 17.Which term of the AP 2, 9, 16, 23, … is 149? (a) 23rd (b) 22nd (c) 24th (d) 21st
  18. 18.What is the 18th term of the AP 4, 7, 10, 13, …? (a) 54 (b) 55 (c) 51 (d) 58
  19. 19.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28
  20. 20.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 225 (b) 414 (c) 39 (d) 207
  21. 21.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 20 (b) 19 (c) 21 (d) 24
  22. 22.Which term of the AP 9, 15, 21, 27, … is 129? (a) 20th (b) 22nd (c) 23rd (d) 21st
  23. 23.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 13 (b) 10 (c) 11 (d) 12
  24. 24.What is the 35th term of the AP 12, 21, 30, 39, …? (a) 327 (b) 318 (c) 306 (d) 315
  25. 25.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 1036 (c) 2070 (d) 990
  26. 26.Which term of the AP 6, 8, 10, 12, … is 20? (a) 8th (b) 9th (c) 10th (d) 7th
  27. 27.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 22 (b) 25 (c) 20 (d) 21
  28. 28.What is the 11th term of the AP 2, 5, 8, 11, …? (a) 35 (b) 32 (c) 30 (d) 33
  29. 29.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 92 (b) 184 (c) 15 (d) 96
  30. 30.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 66 (b) 120 (c) 15 (d) 60
  31. 31.What is the 34th term of the AP 11, 18, 25, 32, …? (a) 242 (b) 238 (c) 231 (d) 249
  32. 32.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 12 (c) 45 (d) 80
  33. 33.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 77 (b) 78 (c) 154 (d) 14
  34. 34.What is the 27th term of the AP 20, 24, 28, 32, …? (a) 108 (b) 124 (c) 128 (d) 104
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  36. 36.What is the 17th term of the AP 17, 24, 31, 38, …? (a) 119 (b) 129 (c) 112 (d) 136
  37. 37.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 220 (b) 440 (c) 231 (d) 30
  38. 38.Which term of the AP 3, 7, 11, 15, … is 79? (a) 19th (b) 20th (c) 21st (d) 22nd
  39. 39.Which term of the AP 4, 7, 10, 13, … is 46? (a) 17th (b) 15th (c) 16th (d) 14th
  40. 40.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 10 (c) 60 (d) 55

Answer key

  1. 1081
  2. 900
  3. 64
  4. 132
  5. 23
  6. 282
  7. 4753
  8. 94
  9. 88
  10. 123
  11. 128
  12. 33
  13. 55
  14. 16
  15. 26th
  16. 21st
  17. 22nd
  18. 55
  19. 49
  20. 207
  21. 20
  22. 21st
  23. 11
  24. 318
  25. 1035
  26. 8th
  27. 21
  28. 32
  29. 92
  30. 60
  31. 242
  32. 40
  33. 77
  34. 124
  35. 100
  36. 129
  37. 220
  38. 20th
  39. 15th
  40. 55

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