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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 642 · 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 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  2. 2.What is the 35th term of the AP 5, 12, 19, 26, …? (a) 250 (b) 238 (c) 243 (d) 245
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42
  4. 4.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 2070 (c) 1036 (d) 1035
  5. 5.What is the 25th term of the AP 19, 27, 35, 43, …? (a) 219 (b) 200 (c) 211 (d) 192
  6. 6.What is the 12th term of the AP 20, 24, 28, 32, …? (a) 44 (b) 64 (c) 68 (d) 48
  7. 7.What is the 15th term of the AP 4, 9, 14, 19, …? (a) 75 (b) 74 (c) 79 (d) 70
  8. 8.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 50 (c) 110 (d) 45
  9. 9.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 39 (b) 540 (c) 288 (d) 270
  10. 10.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 220 (b) 110 (c) 34 (d) 125
  11. 11.Which term of the AP 15, 21, 27, 33, … is 111? (a) 18th (b) 19th (c) 16th (d) 17th
  12. 12.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 12 (b) 14 (c) 13 (d) 11
  13. 13.Which term of the AP 4, 12, 20, 28, … is 196? (a) 24th (b) 27th (c) 26th (d) 25th
  14. 14.Which term of the AP 10, 15, 20, 25, … is 110? (a) 20th (b) 22nd (c) 21st (d) 23rd
  15. 15.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 4656 (d) 9312
  16. 16.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 28 (b) 27 (c) 29 (d) 37
  17. 17.What is the 30th term of the AP 20, 23, 26, 29, …? (a) 110 (b) 87 (c) 107 (d) 90
  18. 18.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 208 (b) 204 (c) 198 (d) 202
  19. 19.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 31 (b) 35 (c) 30 (d) 29
  20. 20.Which term of the AP 19, 25, 31, 37, … is 235? (a) 38th (b) 39th (c) 36th (d) 37th
  21. 21.What is the 39th term of the AP 16, 22, 28, 34, …? (a) 234 (b) 250 (c) 244 (d) 228
  22. 22.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 400 (b) 200 (c) 38 (d) 220
  23. 23.What is the 33rd term of the AP 3, 5, 7, 9, …? (a) 66 (b) 69 (c) 64 (d) 67
  24. 24.What is the 23rd term of the AP 18, 23, 28, 33, …? (a) 110 (b) 115 (c) 128 (d) 133
  25. 25.What is the 36th term of the AP 2, 7, 12, 17, …? (a) 177 (b) 180 (c) 175 (d) 182
  26. 26.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 33 (b) 34 (c) 41 (d) 32
  27. 27.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 50 (c) 26 (d) 7
  28. 28.What is the 34th term of the AP 11, 13, 15, 17, …? (a) 66 (b) 77 (c) 79 (d) 68
  29. 29.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 231 (c) 506 (d) 242
  30. 30.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 24 (b) 108 (c) 210 (d) 105
  31. 31.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 156 (b) 78 (c) 84 (d) 12
  32. 32.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 26 (b) 27 (c) 34 (d) 25
  33. 33.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 192 (b) 189 (c) 378 (d) 33
  34. 34.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 132 (b) 37 (c) 264 (d) 150
  35. 35.What is the missing term in the AP 7, ?, 23, 31, 39? (a) 15 (b) 16 (c) 14 (d) 23
  36. 36.What is the missing term in the AP 19, 21, ?, 25, 27? (a) 22 (b) 23 (c) 24 (d) 25
  37. 37.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 129 (b) 252 (c) 26 (d) 126
  38. 38.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  39. 39.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 37 (b) 38 (c) 39 (d) 44
  40. 40.Which term of the AP 15, 20, 25, 30, … is 155? (a) 28th (b) 30th (c) 31st (d) 29th

Answer key

  1. 625
  2. 243
  3. 36
  4. 1035
  5. 211
  6. 64
  7. 74
  8. 55
  9. 270
  10. 110
  11. 17th
  12. 12
  13. 25th
  14. 21st
  15. 4656
  16. 28
  17. 107
  18. 202
  19. 30
  20. 37th
  21. 244
  22. 200
  23. 67
  24. 128
  25. 177
  26. 33
  27. 25
  28. 77
  29. 253
  30. 105
  31. 78
  32. 26
  33. 189
  34. 132
  35. 15
  36. 23
  37. 126
  38. 576
  39. 38
  40. 29th

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