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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 645 · 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 12 terms of the AP 6, 11, 16, …? (a) 432 (b) 61 (c) 804 (d) 402
  2. 2.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 23 (b) 20 (c) 18 (d) 19
  3. 3.Which term of the AP 2, 4, 6, 8, … is 76? (a) 38th (b) 40th (c) 37th (d) 39th
  4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  5. 5.Which term of the AP 6, 13, 20, 27, … is 265? (a) 37th (b) 38th (c) 40th (d) 39th
  6. 6.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 40 (b) 168 (c) 300 (d) 150
  7. 7.What is the 34th term of the AP 10, 15, 20, 25, …? (a) 175 (b) 170 (c) 165 (d) 180
  8. 8.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 4 (b) 5 (c) 8 (d) 6
  9. 9.Which term of the AP 1, 7, 13, 19, … is 49? (a) 9th (b) 10th (c) 8th (d) 11th
  10. 10.Which term of the AP 8, 15, 22, 29, … is 64? (a) 8th (b) 10th (c) 9th (d) 11th
  11. 11.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 20 (b) 19 (c) 22 (d) 18
  12. 12.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 11 (b) 126 (c) 64 (d) 63
  13. 13.Which term of the AP 9, 18, 27, 36, … is 153? (a) 16th (b) 19th (c) 18th (d) 17th
  14. 14.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 17 (b) 15 (c) 23 (d) 16
  15. 15.Which term of the AP 1, 4, 7, 10, … is 118? (a) 40th (b) 41st (c) 42nd (d) 39th
  16. 16.Which term of the AP 15, 23, 31, 39, … is 159? (a) 21st (b) 19th (c) 18th (d) 20th
  17. 17.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 156 (d) 78
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 240 (d) 120
  19. 19.Which term of the AP 6, 9, 12, 15, … is 48? (a) 14th (b) 16th (c) 15th (d) 17th
  20. 20.Which term of the AP 3, 6, 9, 12, … is 33? (a) 13th (b) 11th (c) 10th (d) 12th
  21. 21.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 18 (b) 20 (c) 25 (d) 19
  22. 22.What is the 22nd term of the AP 11, 17, 23, 29, …? (a) 137 (b) 143 (c) 126 (d) 132
  23. 23.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 17 (b) 13 (c) 12 (d) 14
  24. 24.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 19 (b) 18 (c) 25 (d) 17
  25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
  26. 26.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 9 (b) 8 (c) 12 (d) 10
  27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  28. 28.What is the 33rd term of the AP 20, 28, 36, 44, …? (a) 284 (b) 264 (c) 276 (d) 256
  29. 29.What is the 39th term of the AP 14, 21, 28, 35, …? (a) 280 (b) 273 (c) 266 (d) 287
  30. 30.What is the 32nd term of the AP 5, 10, 15, 20, …? (a) 155 (b) 165 (c) 161 (d) 160
  31. 31.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 17 (c) 77 (d) 84
  32. 32.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 75 (b) 21 (c) 78 (d) 150
  33. 33.What is the 11th term of the AP 5, 13, 21, 29, …? (a) 85 (b) 93 (c) 80 (d) 88
  34. 34.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 55 (c) 50 (d) 45
  35. 35.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  36. 36.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 24 (b) 25 (c) 26 (d) 28
  37. 37.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 198 (b) 99 (c) 14 (d) 100
  38. 38.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 275 (b) 50 (c) 550 (d) 300
  39. 39.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 6480 (c) 3200 (d) 3160
  40. 40.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 24 (b) 25 (c) 27 (d) 23

Answer key

  1. 402
  2. 19
  3. 38th
  4. 529
  5. 38th
  6. 150
  7. 175
  8. 5
  9. 9th
  10. 9th
  11. 19
  12. 63
  13. 17th
  14. 16
  15. 40th
  16. 19th
  17. 144
  18. 225
  19. 15th
  20. 11th
  21. 19
  22. 137
  23. 13
  24. 18
  25. 441
  26. 9
  27. 121
  28. 276
  29. 280
  30. 160
  31. 77
  32. 75
  33. 85
  34. 55
  35. 400
  36. 25
  37. 99
  38. 275
  39. 3240
  40. 24

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