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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 567 · 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 17, 26, 35, 44, … is 314? (a) 33rd (b) 36th (c) 34th (d) 35th
  2. 2.Which term of the AP 1, 9, 17, 25, … is 225? (a) 28th (b) 30th (c) 29th (d) 31st
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 210 (d) 27
  4. 4.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 154 (c) 77 (d) 78
  5. 5.What is the 27th term of the AP 20, 23, 26, 29, …? (a) 98 (b) 81 (c) 101 (d) 78
  6. 6.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 75 (b) 80 (c) 150 (d) 25
  7. 7.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 10100 (c) 5050 (d) 4950
  8. 8.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 31 (b) 30 (c) 38 (d) 29
  9. 9.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 20 (b) 24 (c) 21 (d) 22
  10. 10.What is the 10th term of the AP 9, 11, 13, 15, …? (a) 18 (b) 20 (c) 27 (d) 29
  11. 11.What is the 13th term of the AP 8, 17, 26, 35, …? (a) 116 (b) 117 (c) 125 (d) 108
  12. 12.Which term of the AP 2, 4, 6, 8, … is 64? (a) 32nd (b) 34th (c) 31st (d) 33rd
  13. 13.What is the 39th term of the AP 5, 11, 17, 23, …? (a) 234 (b) 228 (c) 239 (d) 233
  14. 14.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3362 (c) 6806 (d) 3321
  15. 15.What is the 17th term of the AP 14, 19, 24, 29, …? (a) 94 (b) 85 (c) 99 (d) 80
  16. 16.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 105 (b) 120 (c) 210 (d) 33
  17. 17.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 10 (b) 8 (c) 11 (d) 9
  18. 18.What is the 32nd term of the AP 12, 14, 16, 18, …? (a) 74 (b) 62 (c) 64 (d) 76
  19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 120 (c) 240 (d) 29
  20. 20.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 24 (b) 216 (c) 108 (d) 120
  21. 21.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
  22. 22.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 34 (b) 43 (c) 35 (d) 36
  23. 23.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 156 (b) 144 (c) 288 (d) 23
  24. 24.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 23 (b) 25 (c) 22 (d) 24
  25. 25.What is the missing term in the AP 20, ?, 36, 44, 52? (a) 27 (b) 28 (c) 29 (d) 36
  26. 26.What is the 31st term of the AP 6, 12, 18, 24, …? (a) 192 (b) 180 (c) 186 (d) 187
  27. 27.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 16 (b) 21 (c) 14 (d) 15
  28. 28.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 21 (b) 24 (c) 20 (d) 19
  29. 29.Which term of the AP 19, 23, 27, 31, … is 119? (a) 28th (b) 26th (c) 27th (d) 25th
  30. 30.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 326 (c) 300 (d) 325
  31. 31.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 136 (b) 128 (c) 256 (d) 23
  32. 32.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  33. 33.What is the 16th term of the AP 8, 17, 26, 35, …? (a) 143 (b) 135 (c) 152 (d) 144
  34. 34.What is the 37th term of the AP 13, 21, 29, 37, …? (a) 288 (b) 301 (c) 296 (d) 309
  35. 35.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 171 (c) 153 (d) 162
  36. 36.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 16 (b) 24 (c) 18 (d) 17
  37. 37.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 234 (b) 117 (c) 132 (d) 32
  38. 38.Which term of the AP 1, 9, 17, 25, … is 145? (a) 18th (b) 20th (c) 21st (d) 19th
  39. 39.What is the 40th term of the AP 19, 22, 25, 28, …? (a) 117 (b) 120 (c) 136 (d) 139
  40. 40.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 51 (b) 60 (c) 102 (d) 16

Answer key

  1. 34th
  2. 29th
  3. 196
  4. 77
  5. 98
  6. 75
  7. 5050
  8. 30
  9. 21
  10. 27
  11. 116
  12. 32nd
  13. 233
  14. 3403
  15. 94
  16. 105
  17. 9
  18. 74
  19. 225
  20. 108
  21. 49
  22. 35
  23. 144
  24. 23
  25. 28
  26. 186
  27. 15
  28. 20
  29. 26th
  30. 325
  31. 128
  32. 361
  33. 143
  34. 301
  35. 171
  36. 17
  37. 117
  38. 19th
  39. 136
  40. 51

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