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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 298 · 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 2, 8, 14, …? (a) 26 (b) 70 (c) 85 (d) 140
  2. 2.What is the 18th term of the AP 10, 15, 20, 25, …? (a) 90 (b) 95 (c) 100 (d) 85
  3. 3.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 17 (b) 22 (c) 19 (d) 18
  4. 4.What is the 37th term of the AP 13, 20, 27, 34, …? (a) 272 (b) 265 (c) 259 (d) 252
  5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 49 (d) 56
  6. 6.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 650 (d) 49
  7. 7.What is the missing term in the AP 2, 9, ?, 23, 30? (a) 17 (b) 15 (c) 23 (d) 16
  8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 441 (d) 41
  9. 9.Which term of the AP 9, 14, 19, 24, … is 54? (a) 9th (b) 11th (c) 10th (d) 12th
  10. 10.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 90 (c) 91 (d) 180
  11. 11.Which term of the AP 1, 3, 5, 7, … is 53? (a) 26th (b) 29th (c) 27th (d) 28th
  12. 12.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 153 (c) 154 (d) 306
  13. 13.What is the 29th term of the AP 6, 10, 14, 18, …? (a) 112 (b) 122 (c) 118 (d) 116
  14. 14.What is the 31st term of the AP 15, 23, 31, 39, …? (a) 248 (b) 263 (c) 255 (d) 240
  15. 15.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 88 (b) 84 (c) 100 (d) 104
  16. 16.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 13 (b) 8 (c) 7 (d) 6
  17. 17.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 198 (b) 209 (c) 396 (d) 28
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 272 (c) 31 (d) 136
  19. 19.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 224 (b) 46 (c) 400 (d) 200
  20. 20.What is the 13th term of the AP 6, 9, 12, 15, …? (a) 45 (b) 36 (c) 39 (d) 42
  21. 21.What is the 17th term of the AP 12, 19, 26, 33, …? (a) 124 (b) 131 (c) 112 (d) 119
  22. 22.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 16 (b) 13 (c) 15 (d) 14
  23. 23.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 32 (b) 30 (c) 39 (d) 31
  24. 24.What is the missing term in the AP 4, ?, 16, 22, 28? (a) 16 (b) 9 (c) 10 (d) 11
  25. 25.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 52 (b) 279 (c) 504 (d) 252
  26. 26.What is the missing term in the AP 6, 11, 16, ?, 26? (a) 26 (b) 20 (c) 22 (d) 21
  27. 27.Which term of the AP 17, 20, 23, 26, … is 47? (a) 11th (b) 12th (c) 10th (d) 13th
  28. 28.What is the 34th term of the AP 7, 16, 25, 34, …? (a) 304 (b) 313 (c) 297 (d) 306
  29. 29.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 128 (c) 120 (d) 136
  30. 30.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 26 (b) 24 (c) 22 (d) 23
  31. 31.What is the 14th term of the AP 14, 19, 24, 29, …? (a) 65 (b) 84 (c) 70 (d) 79
  32. 32.Which term of the AP 3, 7, 11, 15, … is 59? (a) 14th (b) 16th (c) 15th (d) 17th
  33. 33.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 216 (b) 196 (c) 392 (d) 42
  34. 34.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3042 (c) 3081 (d) 6162
  35. 35.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 29 (b) 24 (c) 25 (d) 23
  36. 36.What is the 26th term of the AP 5, 13, 21, 29, …? (a) 208 (b) 205 (c) 213 (d) 200
  37. 37.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 2450 (d) 1225
  38. 38.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 21 (b) 20 (c) 22 (d) 25
  39. 39.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 462 (c) 232 (d) 231
  40. 40.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 44 (b) 45 (c) 54 (d) 46

Answer key

  1. 70
  2. 95
  3. 18
  4. 265
  5. 49
  6. 625
  7. 16
  8. 441
  9. 10th
  10. 90
  11. 27th
  12. 153
  13. 118
  14. 255
  15. 100
  16. 7
  17. 198
  18. 256
  19. 200
  20. 42
  21. 124
  22. 14
  23. 31
  24. 10
  25. 252
  26. 21
  27. 11th
  28. 304
  29. 136
  30. 23
  31. 79
  32. 15th
  33. 196
  34. 3081
  35. 24
  36. 205
  37. 1225
  38. 21
  39. 231
  40. 45

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