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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 603 · 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 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 81 (d) 17
  2. 2.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 264 (c) 150 (d) 132
  3. 3.What is the 29th term of the AP 1, 10, 19, 28, …? (a) 252 (b) 253 (c) 262 (d) 261
  4. 4.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 150 (b) 75 (c) 20 (d) 84
  5. 5.What is the 10th term of the AP 8, 14, 20, 26, …? (a) 60 (b) 62 (c) 68 (d) 54
  6. 6.What is the 12th term of the AP 3, 8, 13, 18, …? (a) 60 (b) 63 (c) 55 (d) 58
  7. 7.What is the 38th term of the AP 10, 18, 26, 34, …? (a) 314 (b) 296 (c) 304 (d) 306
  8. 8.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 36 (b) 44 (c) 35 (d) 37
  9. 9.What is the 10th term of the AP 13, 20, 27, 34, …? (a) 63 (b) 70 (c) 83 (d) 76
  10. 10.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 1122 (c) 561 (d) 528
  11. 11.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 63 (c) 64 (d) 11
  12. 12.What is the 21st term of the AP 16, 18, 20, 22, …? (a) 56 (b) 58 (c) 42 (d) 40
  13. 13.What is the missing term in the AP 4, ?, 16, 22, 28? (a) 11 (b) 16 (c) 10 (d) 9
  14. 14.What is the missing term in the AP 19, 22, 25, ?, 31? (a) 28 (b) 27 (c) 29 (d) 31
  15. 15.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 108 (b) 24 (c) 99 (d) 198
  16. 16.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 820 (c) 780 (d) 800
  17. 17.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 300 (b) 275 (c) 550 (d) 50
  18. 18.What is the 16th term of the AP 16, 21, 26, 31, …? (a) 96 (b) 75 (c) 80 (d) 91
  19. 19.What is the 21st term of the AP 6, 13, 20, 27, …? (a) 147 (b) 153 (c) 146 (d) 140
  20. 20.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 180 (b) 90 (c) 105 (d) 30
  21. 21.Which term of the AP 3, 6, 9, 12, … is 111? (a) 36th (b) 38th (c) 39th (d) 37th
  22. 22.Which term of the AP 8, 16, 24, 32, … is 224? (a) 29th (b) 27th (c) 30th (d) 28th
  23. 23.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 144 (c) 80 (d) 72
  24. 24.What is the 19th term of the AP 19, 28, 37, 46, …? (a) 162 (b) 190 (c) 171 (d) 181
  25. 25.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 240 (c) 120 (d) 105
  26. 26.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 63 (c) 13 (d) 126
  27. 27.What is the 37th term of the AP 14, 18, 22, 26, …? (a) 162 (b) 144 (c) 158 (d) 148
  28. 28.What is the 17th term of the AP 10, 13, 16, 19, …? (a) 48 (b) 61 (c) 58 (d) 51
  29. 29.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 15 (b) 14 (c) 16 (d) 19
  30. 30.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 31 (b) 30 (c) 29 (d) 36
  31. 31.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 77 (b) 78 (c) 154 (d) 12
  32. 32.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 11 (d) 36
  33. 33.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 8 (b) 6 (c) 9 (d) 7
  34. 34.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 2146 (c) 4290 (d) 2145
  35. 35.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 35 (b) 220 (c) 223 (d) 440
  36. 36.What is the 21st term of the AP 4, 9, 14, 19, …? (a) 105 (b) 109 (c) 104 (d) 100
  37. 37.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 12 (b) 11 (c) 13 (d) 10
  38. 38.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 23 (b) 20 (c) 18 (d) 19
  39. 39.What is the 34th term of the AP 13, 19, 25, 31, …? (a) 198 (b) 204 (c) 211 (d) 217
  40. 40.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 67 (b) 814 (c) 407 (d) 440

Answer key

  1. 81
  2. 132
  3. 253
  4. 75
  5. 62
  6. 58
  7. 306
  8. 36
  9. 76
  10. 561
  11. 63
  12. 56
  13. 10
  14. 28
  15. 99
  16. 820
  17. 275
  18. 91
  19. 146
  20. 90
  21. 37th
  22. 28th
  23. 72
  24. 181
  25. 120
  26. 63
  27. 158
  28. 58
  29. 15
  30. 30
  31. 77
  32. 36
  33. 7
  34. 2145
  35. 220
  36. 104
  37. 11
  38. 19
  39. 211
  40. 407

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