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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 675 · 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 29th term of the AP 10, 19, 28, 37, …? (a) 261 (b) 252 (c) 271 (d) 262
  2. 2.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 18 (c) 120 (d) 60
  3. 3.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 38 (b) 39 (c) 37 (d) 46
  4. 4.What is the 34th term of the AP 3, 5, 7, 9, …? (a) 68 (b) 66 (c) 69 (d) 71
  5. 5.Which term of the AP 3, 6, 9, 12, … is 33? (a) 12th (b) 10th (c) 11th (d) 13th
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  7. 7.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 1540 (c) 3080 (d) 1541
  8. 8.What is the 36th term of the AP 4, 7, 10, 13, …? (a) 112 (b) 109 (c) 108 (d) 105
  9. 9.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 426 (b) 852 (c) 456 (d) 63
  10. 10.Which term of the AP 9, 18, 27, 36, … is 126? (a) 14th (b) 13th (c) 15th (d) 16th
  11. 11.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 18 (b) 17 (c) 19 (d) 23
  12. 12.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 2926 (c) 3003 (d) 3004
  13. 13.Which term of the AP 18, 20, 22, 24, … is 82? (a) 41st (b) 33rd (c) 32nd (d) 34th
  14. 14.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  15. 15.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 220 (c) 20 (d) 110
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  17. 17.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 30 (b) 20 (c) 22 (d) 21
  18. 18.What is the 11th term of the AP 10, 19, 28, 37, …? (a) 99 (b) 90 (c) 100 (d) 109
  19. 19.What is the 37th term of the AP 13, 19, 25, 31, …? (a) 229 (b) 235 (c) 222 (d) 216
  20. 20.Which term of the AP 10, 15, 20, 25, … is 100? (a) 20th (b) 21st (c) 18th (d) 19th
  21. 21.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 24 (b) 22 (c) 21 (d) 20
  22. 22.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 220 (b) 45 (c) 240 (d) 440
  23. 23.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 390 (b) 420 (c) 780 (d) 60
  24. 24.What is the 24th term of the AP 7, 16, 25, 34, …? (a) 216 (b) 214 (c) 223 (d) 207
  25. 25.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 7482 (d) 3655
  26. 26.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 66 (c) 36 (d) 33
  27. 27.What is the 14th term of the AP 7, 11, 15, 19, …? (a) 52 (b) 56 (c) 59 (d) 63
  28. 28.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 120 (b) 224 (c) 21 (d) 112
  29. 29.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 33 (b) 252 (c) 126 (d) 131
  30. 30.What is the 20th term of the AP 19, 21, 23, 25, …? (a) 40 (b) 59 (c) 38 (d) 57
  31. 31.Which term of the AP 19, 26, 33, 40, … is 131? (a) 16th (b) 18th (c) 19th (d) 17th
  32. 32.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  33. 33.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 55 (d) 110
  34. 34.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 42 (b) 43 (c) 9 (d) 84
  35. 35.Which term of the AP 19, 28, 37, 46, … is 109? (a) 11th (b) 10th (c) 12th (d) 13th
  36. 36.What is the 37th term of the AP 4, 11, 18, 25, …? (a) 252 (b) 259 (c) 256 (d) 263
  37. 37.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 930 (d) 59
  38. 38.Which term of the AP 10, 14, 18, 22, … is 166? (a) 39th (b) 42nd (c) 41st (d) 40th
  39. 39.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 65 (b) 130 (c) 17 (d) 70
  40. 40.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 154 (b) 37 (c) 133 (d) 266

Answer key

  1. 262
  2. 60
  3. 38
  4. 69
  5. 11th
  6. 81
  7. 1540
  8. 109
  9. 426
  10. 14th
  11. 18
  12. 3003
  13. 33rd
  14. 361
  15. 110
  16. 729
  17. 21
  18. 100
  19. 229
  20. 19th
  21. 21
  22. 220
  23. 390
  24. 214
  25. 3741
  26. 33
  27. 59
  28. 112
  29. 126
  30. 57
  31. 17th
  32. 400
  33. 55
  34. 42
  35. 11th
  36. 256
  37. 900
  38. 40th
  39. 65
  40. 133

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