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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 16 · 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 20, 28, 36, 44, … is 332? (a) 39th (b) 41st (c) 40th (d) 42nd
  2. 2.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 435 (d) 57
  3. 3.What is the 15th term of the AP 11, 18, 25, 32, …? (a) 109 (b) 98 (c) 116 (d) 105
  4. 4.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 13 (b) 8 (c) 9 (d) 10
  5. 5.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 43 (b) 212 (c) 414 (d) 207
  6. 6.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 23 (b) 196 (c) 98 (d) 101
  7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 53 (d) 729
  8. 8.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 145 (b) 140 (c) 35 (d) 280
  9. 9.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 210 (c) 98 (d) 91
  10. 10.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 51 (b) 100 (c) 50 (d) 12
  11. 11.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4754 (c) 4753 (d) 9506
  12. 12.What is the 13th term of the AP 11, 16, 21, 26, …? (a) 65 (b) 71 (c) 76 (d) 60
  13. 13.What is the 38th term of the AP 10, 14, 18, 22, …? (a) 162 (b) 152 (c) 148 (d) 158
  14. 14.What is the 16th term of the AP 7, 12, 17, 22, …? (a) 80 (b) 75 (c) 87 (d) 82
  15. 15.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 225 (b) 252 (c) 49 (d) 450
  16. 16.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 21 (b) 15 (c) 17 (d) 16
  17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
  18. 18.Which term of the AP 16, 20, 24, 28, … is 140? (a) 35th (b) 32nd (c) 33rd (d) 31st
  19. 19.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 903 (c) 1806 (d) 882
  20. 20.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 42 (c) 11 (d) 36
  21. 21.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 100 (d) 55
  22. 22.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 26 (b) 324 (c) 162 (d) 171
  23. 23.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 85 (b) 140 (c) 26 (d) 70
  24. 24.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 248 (b) 26 (c) 124 (d) 136
  25. 25.Which term of the AP 5, 7, 9, 11, … is 83? (a) 41st (b) 40th (c) 42nd (d) 39th
  26. 26.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3403 (c) 6972 (d) 3486
  27. 27.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 14 (b) 56 (c) 63 (d) 112
  28. 28.Which term of the AP 19, 21, 23, 25, … is 81? (a) 34th (b) 33rd (c) 32nd (d) 31st
  29. 29.What is the 16th term of the AP 13, 18, 23, 28, …? (a) 75 (b) 88 (c) 93 (d) 80
  30. 30.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 14 (b) 20 (c) 13 (d) 15
  31. 31.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 288 (c) 600 (d) 276
  32. 32.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3081 (c) 6162 (d) 3042
  33. 33.What is the 37th term of the AP 4, 6, 8, 10, …? (a) 78 (b) 76 (c) 72 (d) 74
  34. 34.What is the 22nd term of the AP 11, 13, 15, 17, …? (a) 53 (b) 44 (c) 42 (d) 55
  35. 35.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 304 (b) 33 (c) 152 (d) 168
  36. 36.Which term of the AP 8, 16, 24, 32, … is 128? (a) 15th (b) 17th (c) 18th (d) 16th
  37. 37.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 18 (b) 16 (c) 25 (d) 17
  38. 38.Which term of the AP 13, 20, 27, 34, … is 153? (a) 23rd (b) 21st (c) 22nd (d) 20th
  39. 39.What is the 39th term of the AP 8, 15, 22, 29, …? (a) 273 (b) 281 (c) 274 (d) 266
  40. 40.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 280 (b) 23 (c) 140 (d) 150

Answer key

  1. 40th
  2. 841
  3. 109
  4. 9
  5. 207
  6. 98
  7. 729
  8. 140
  9. 105
  10. 50
  11. 4753
  12. 71
  13. 158
  14. 82
  15. 225
  16. 16
  17. 121
  18. 32nd
  19. 903
  20. 36
  21. 100
  22. 162
  23. 70
  24. 124
  25. 40th
  26. 3486
  27. 56
  28. 32nd
  29. 88
  30. 14
  31. 300
  32. 3081
  33. 76
  34. 53
  35. 152
  36. 16th
  37. 17
  38. 21st
  39. 274
  40. 140

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