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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 172 · 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 42? (a) 861 (b) 1806 (c) 903 (d) 882
  2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 650 (d) 325
  3. 3.What is the 37th term of the AP 19, 21, 23, 25, …? (a) 93 (b) 72 (c) 74 (d) 91
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  5. 5.Which term of the AP 11, 13, 15, 17, … is 25? (a) 10th (b) 9th (c) 8th (d) 7th
  6. 6.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 190 (c) 191 (d) 171
  7. 7.What is the 23rd term of the AP 15, 19, 23, 27, …? (a) 88 (b) 92 (c) 103 (d) 107
  8. 8.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 23 (b) 24 (c) 22 (d) 28
  9. 9.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 80 (c) 72 (d) 16
  10. 10.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 462 (b) 69 (c) 429 (d) 858
  11. 11.What is the missing term in the AP 2, ?, 16, 23, 30? (a) 8 (b) 9 (c) 16 (d) 10
  12. 12.What is the 19th term of the AP 20, 27, 34, 41, …? (a) 153 (b) 126 (c) 133 (d) 146
  13. 13.What is the 24th term of the AP 11, 18, 25, 32, …? (a) 168 (b) 161 (c) 172 (d) 179
  14. 14.What is the 25th term of the AP 20, 23, 26, 29, …? (a) 95 (b) 75 (c) 72 (d) 92
  15. 15.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 6 (b) 11 (c) 8 (d) 7
  16. 16.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4950 (c) 4851 (d) 4951
  17. 17.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 35 (b) 270 (c) 150 (d) 135
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 90 (d) 17
  19. 19.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 204 (b) 102 (c) 120 (d) 32
  20. 20.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 15 (d) 64
  21. 21.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 36 (b) 35 (c) 43 (d) 34
  22. 22.What is the sum of the first 7 terms of the AP 3, 6, 9, …? (a) 87 (b) 168 (c) 84 (d) 21
  23. 23.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 216 (c) 228 (d) 29
  24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
  25. 25.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 11 (c) 63 (d) 64
  26. 26.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 28 (b) 396 (c) 209 (d) 198
  27. 27.What is the 18th term of the AP 3, 11, 19, 27, …? (a) 147 (b) 144 (c) 139 (d) 136
  28. 28.What is the sum of the first 12 terms of the AP 5, 11, 17, …? (a) 492 (b) 71 (c) 912 (d) 456
  29. 29.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 9 (b) 46 (c) 45 (d) 90
  30. 30.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 118 (c) 17 (d) 117
  31. 31.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 62 (b) 380 (c) 350 (d) 700
  32. 32.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 77 (b) 140 (c) 70 (d) 16
  33. 33.Which term of the AP 6, 14, 22, 30, … is 318? (a) 42nd (b) 41st (c) 39th (d) 40th
  34. 34.Which term of the AP 18, 27, 36, 45, … is 225? (a) 25th (b) 23rd (c) 26th (d) 24th
  35. 35.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 170 (b) 160 (c) 320 (d) 25
  36. 36.What is the 22nd term of the AP 13, 17, 21, 25, …? (a) 101 (b) 97 (c) 84 (d) 88
  37. 37.What is the 37th term of the AP 11, 13, 15, 17, …? (a) 83 (b) 85 (c) 74 (d) 72
  38. 38.What is the 19th term of the AP 8, 11, 14, 17, …? (a) 65 (b) 57 (c) 54 (d) 62
  39. 39.What is the missing term in the AP 10, 19, ?, 37, 46? (a) 27 (b) 28 (c) 37 (d) 29
  40. 40.Which term of the AP 11, 20, 29, 38, … is 83? (a) 11th (b) 10th (c) 9th (d) 8th

Answer key

  1. 903
  2. 625
  3. 91
  4. 25
  5. 8th
  6. 190
  7. 103
  8. 23
  9. 72
  10. 429
  11. 9
  12. 146
  13. 172
  14. 92
  15. 7
  16. 4950
  17. 135
  18. 81
  19. 102
  20. 64
  21. 35
  22. 84
  23. 216
  24. 121
  25. 63
  26. 198
  27. 139
  28. 456
  29. 45
  30. 117
  31. 350
  32. 70
  33. 40th
  34. 24th
  35. 160
  36. 97
  37. 83
  38. 62
  39. 28
  40. 9th

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