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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 27 · 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 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 9 (d) 30
  2. 2.Which term of the AP 4, 10, 16, 22, … is 118? (a) 20th (b) 21st (c) 22nd (d) 19th
  3. 3.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 63 (c) 126 (d) 13
  4. 4.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 5112 (c) 2557 (d) 2485
  5. 5.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 1596 (c) 1654 (d) 3306
  6. 6.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 3004 (c) 2926 (d) 6006
  7. 7.What is the sum of all the whole numbers from 1 to 88? (a) 3916 (b) 3828 (c) 3872 (d) 7832
  8. 8.What is the 14th term of the AP 16, 22, 28, 34, …? (a) 100 (b) 78 (c) 84 (d) 94
  9. 9.Which term of the AP 7, 9, 11, 13, … is 33? (a) 13th (b) 14th (c) 16th (d) 15th
  10. 10.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 2738 (c) 5550 (d) 2775
  11. 11.What is the 12th term of the AP 1, 3, 5, 7, …? (a) 25 (b) 22 (c) 23 (d) 24
  12. 12.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 53 (b) 610 (c) 330 (d) 305
  13. 13.What is the 11th term of the AP 10, 13, 16, 19, …? (a) 33 (b) 30 (c) 43 (d) 40
  14. 14.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 18 (b) 78 (c) 156 (d) 84
  15. 15.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 26 (b) 27 (c) 28 (d) 34
  16. 16.What is the 14th term of the AP 4, 7, 10, 13, …? (a) 42 (b) 46 (c) 43 (d) 39
  17. 17.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 176 (b) 89 (c) 13 (d) 88
  18. 18.What is the 26th term of the AP 20, 29, 38, 47, …? (a) 234 (b) 225 (c) 254 (d) 245
  19. 19.Which term of the AP 16, 23, 30, 37, … is 219? (a) 32nd (b) 31st (c) 30th (d) 29th
  20. 20.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 240 (b) 120 (c) 30 (d) 132
  21. 21.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 90 (b) 15 (c) 45 (d) 48
  22. 22.Which term of the AP 19, 21, 23, 25, … is 87? (a) 34th (b) 35th (c) 37th (d) 36th
  23. 23.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 23 (b) 22 (c) 21 (d) 20
  24. 24.What is the missing term in the AP 16, 20, 24, ?, 32? (a) 29 (b) 32 (c) 28 (d) 27
  25. 25.What is the 38th term of the AP 5, 14, 23, 32, …? (a) 338 (b) 342 (c) 347 (d) 333
  26. 26.What is the 22nd term of the AP 2, 8, 14, 20, …? (a) 132 (b) 134 (c) 128 (d) 126
  27. 27.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 34 (b) 228 (c) 420 (d) 210
  28. 28.What is the 25th term of the AP 11, 17, 23, 29, …? (a) 150 (b) 161 (c) 144 (d) 155
  29. 29.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 25 (c) 170 (d) 320
  30. 30.What is the 34th term of the AP 14, 21, 28, 35, …? (a) 245 (b) 238 (c) 231 (d) 252
  31. 31.Which term of the AP 10, 12, 14, 16, … is 72? (a) 31st (b) 32nd (c) 36th (d) 33rd
  32. 32.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 3080 (c) 1541 (d) 1540
  33. 33.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 21 (b) 26 (c) 19 (d) 20
  34. 34.What is the missing term in the AP 11, ?, 27, 35, 43? (a) 20 (b) 27 (c) 18 (d) 19
  35. 35.What is the 10th term of the AP 20, 22, 24, 26, …? (a) 18 (b) 40 (c) 20 (d) 38
  36. 36.What is the 22nd term of the AP 8, 16, 24, 32, …? (a) 184 (b) 168 (c) 177 (d) 176
  37. 37.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 14 (b) 17 (c) 12 (d) 13
  38. 38.Which term of the AP 11, 15, 19, 23, … is 67? (a) 17th (b) 14th (c) 15th (d) 16th
  39. 39.What is the 29th term of the AP 16, 20, 24, 28, …? (a) 112 (b) 116 (c) 132 (d) 128
  40. 40.What is the 12th term of the AP 8, 15, 22, 29, …? (a) 77 (b) 92 (c) 84 (d) 85

Answer key

  1. 25
  2. 20th
  3. 63
  4. 2556
  5. 1653
  6. 3003
  7. 3916
  8. 94
  9. 14th
  10. 2775
  11. 23
  12. 305
  13. 40
  14. 78
  15. 27
  16. 43
  17. 88
  18. 245
  19. 30th
  20. 120
  21. 45
  22. 35th
  23. 21
  24. 28
  25. 338
  26. 128
  27. 210
  28. 155
  29. 160
  30. 245
  31. 32nd
  32. 1540
  33. 20
  34. 19
  35. 38
  36. 176
  37. 13
  38. 15th
  39. 128
  40. 85

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