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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 480 · 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 10, 11, 12, …? (a) 120 (b) 61 (c) 14 (d) 60
  2. 2.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 198 (b) 396 (c) 28 (d) 209
  3. 3.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 19 (b) 182 (c) 91 (d) 98
  4. 4.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 44 (b) 34 (c) 35 (d) 36
  5. 5.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 16 (b) 20 (c) 17 (d) 18
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 36 (d) 15
  7. 7.What is the 14th term of the AP 2, 8, 14, 20, …? (a) 86 (b) 78 (c) 80 (d) 84
  8. 8.What is the 21st term of the AP 13, 17, 21, 25, …? (a) 93 (b) 80 (c) 97 (d) 84
  9. 9.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4186 (c) 8556 (d) 4278
  10. 10.Which term of the AP 12, 20, 28, 36, … is 132? (a) 15th (b) 18th (c) 17th (d) 16th
  11. 11.What is the 16th term of the AP 20, 29, 38, 47, …? (a) 144 (b) 135 (c) 155 (d) 164
  12. 12.Which term of the AP 16, 25, 34, 43, … is 79? (a) 8th (b) 9th (c) 10th (d) 7th
  13. 13.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3321 (c) 3403 (d) 3362
  14. 14.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  15. 15.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 73 (b) 70 (c) 140 (d) 20
  16. 16.What is the 11th term of the AP 9, 12, 15, 18, …? (a) 33 (b) 42 (c) 39 (d) 30
  17. 17.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 3741 (c) 3829 (d) 7656
  18. 18.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 96 (c) 192 (d) 114
  19. 19.What is the 36th term of the AP 1, 7, 13, 19, …? (a) 217 (b) 216 (c) 211 (d) 210
  20. 20.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1891 (c) 1892 (d) 1830
  21. 21.What is the 27th term of the AP 9, 14, 19, 24, …? (a) 144 (b) 130 (c) 139 (d) 135
  22. 22.Which term of the AP 18, 25, 32, 39, … is 67? (a) 9th (b) 8th (c) 7th (d) 10th
  23. 23.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  24. 24.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 39 (b) 36 (c) 42 (d) 33
  25. 25.What is the 10th term of the AP 3, 10, 17, 24, …? (a) 63 (b) 70 (c) 73 (d) 66
  26. 26.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 4290 (c) 2145 (d) 2146
  27. 27.Which term of the AP 9, 18, 27, 36, … is 135? (a) 16th (b) 15th (c) 14th (d) 17th
  28. 28.What is the 30th term of the AP 18, 20, 22, 24, …? (a) 78 (b) 58 (c) 76 (d) 60
  29. 29.Which term of the AP 20, 28, 36, 44, … is 172? (a) 19th (b) 22nd (c) 20th (d) 21st
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  31. 31.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 35 (d) 171
  32. 32.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 1326 (c) 2652 (d) 1327
  33. 33.Which term of the AP 3, 11, 19, 27, … is 147? (a) 18th (b) 20th (c) 21st (d) 19th
  34. 34.Which term of the AP 15, 19, 23, 27, … is 131? (a) 32nd (b) 30th (c) 31st (d) 29th
  35. 35.Which term of the AP 1, 6, 11, 16, … is 196? (a) 42nd (b) 40th (c) 41st (d) 39th
  36. 36.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 30 (b) 21 (c) 22 (d) 23
  37. 37.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 9312 (c) 4608 (d) 4656
  38. 38.What is the 25th term of the AP 8, 16, 24, 32, …? (a) 201 (b) 192 (c) 208 (d) 200
  39. 39.What is the 25th term of the AP 1, 3, 5, 7, …? (a) 50 (b) 48 (c) 51 (d) 49
  40. 40.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 21 (b) 23 (c) 29 (d) 22

Answer key

  1. 60
  2. 198
  3. 91
  4. 35
  5. 17
  6. 64
  7. 80
  8. 93
  9. 4278
  10. 16th
  11. 155
  12. 8th
  13. 3403
  14. 441
  15. 70
  16. 39
  17. 3828
  18. 96
  19. 211
  20. 1891
  21. 139
  22. 8th
  23. 49
  24. 39
  25. 66
  26. 2145
  27. 15th
  28. 76
  29. 20th
  30. 100
  31. 324
  32. 1326
  33. 19th
  34. 30th
  35. 40th
  36. 22
  37. 4656
  38. 200
  39. 49
  40. 22

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