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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 73 · 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 missing term in the AP 4, ?, 16, 22, 28? (a) 9 (b) 10 (c) 16 (d) 11
  2. 2.Which term of the AP 9, 18, 27, 36, … is 198? (a) 21st (b) 24th (c) 23rd (d) 22nd
  3. 3.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  4. 4.Which term of the AP 17, 19, 21, 23, … is 47? (a) 15th (b) 18th (c) 17th (d) 16th
  5. 5.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 220 (b) 35 (c) 440 (d) 223
  6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  7. 7.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 13 (b) 12 (c) 15 (d) 11
  8. 8.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 326 (c) 325 (d) 650
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 256 (d) 136
  10. 10.What is the 32nd term of the AP 14, 18, 22, 26, …? (a) 142 (b) 138 (c) 124 (d) 128
  11. 11.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 7 (b) 30 (c) 54 (d) 27
  12. 12.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 60 (c) 16 (d) 65
  13. 13.Which term of the AP 9, 12, 15, 18, … is 93? (a) 30th (b) 28th (c) 31st (d) 29th
  14. 14.Which term of the AP 20, 22, 24, 26, … is 62? (a) 23rd (b) 21st (c) 22nd (d) 31st
  15. 15.What is the 36th term of the AP 2, 4, 6, 8, …? (a) 74 (b) 70 (c) 73 (d) 72
  16. 16.What is the 12th term of the AP 14, 23, 32, 41, …? (a) 99 (b) 108 (c) 122 (d) 113
  17. 17.What is the 27th term of the AP 6, 8, 10, 12, …? (a) 58 (b) 60 (c) 54 (d) 52
  18. 18.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 22 (b) 174 (c) 96 (d) 87
  19. 19.Which term of the AP 2, 5, 8, 11, … is 35? (a) 13th (b) 11th (c) 14th (d) 12th
  20. 20.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3321 (c) 3362 (d) 3403
  21. 21.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 210 (c) 105 (d) 114
  22. 22.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 65 (b) 19 (c) 68 (d) 130
  23. 23.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 282 (b) 564 (c) 300 (d) 40
  24. 24.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 112 (b) 120 (c) 21 (d) 224
  25. 25.Which term of the AP 13, 21, 29, 37, … is 253? (a) 30th (b) 31st (c) 33rd (d) 32nd
  26. 26.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 105 (c) 240 (d) 120
  27. 27.Which term of the AP 18, 27, 36, 45, … is 288? (a) 30th (b) 33rd (c) 32nd (d) 31st
  28. 28.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 34 (b) 44 (c) 35 (d) 36
  29. 29.What is the 32nd term of the AP 5, 13, 21, 29, …? (a) 248 (b) 256 (c) 261 (d) 253
  30. 30.What is the 13th term of the AP 12, 17, 22, 27, …? (a) 65 (b) 77 (c) 60 (d) 72
  31. 31.What is the 30th term of the AP 3, 8, 13, 18, …? (a) 150 (b) 148 (c) 145 (d) 153
  32. 32.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 31 (b) 224 (c) 112 (d) 117
  33. 33.Which term of the AP 8, 12, 16, 20, … is 56? (a) 13th (b) 12th (c) 14th (d) 15th
  34. 34.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 12 (b) 18 (c) 14 (d) 13
  35. 35.What is the 32nd term of the AP 6, 12, 18, 24, …? (a) 198 (b) 193 (c) 192 (d) 186
  36. 36.What is the 12th term of the AP 9, 17, 25, 33, …? (a) 88 (b) 97 (c) 105 (d) 96
  37. 37.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 31 (b) 30 (c) 29 (d) 37
  38. 38.Which term of the AP 14, 21, 28, 35, … is 266? (a) 36th (b) 39th (c) 37th (d) 38th
  39. 39.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 5050 (c) 10100 (d) 4950
  40. 40.What is the 14th term of the AP 7, 9, 11, 13, …? (a) 26 (b) 35 (c) 33 (d) 28

Answer key

  1. 10
  2. 22nd
  3. 100
  4. 16th
  5. 220
  6. 900
  7. 12
  8. 325
  9. 256
  10. 138
  11. 27
  12. 60
  13. 29th
  14. 22nd
  15. 72
  16. 113
  17. 58
  18. 87
  19. 12th
  20. 3403
  21. 105
  22. 65
  23. 282
  24. 112
  25. 31st
  26. 120
  27. 31st
  28. 35
  29. 253
  30. 72
  31. 148
  32. 112
  33. 13th
  34. 13
  35. 192
  36. 97
  37. 30
  38. 37th
  39. 5050
  40. 33

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