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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 754 · 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 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 120 (d) 225
  2. 2.What is the 18th term of the AP 6, 9, 12, 15, …? (a) 51 (b) 60 (c) 57 (d) 54
  3. 3.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 9 (b) 70 (c) 36 (d) 35
  4. 4.What is the sum of all the whole numbers from 1 to 37? (a) 703 (b) 1406 (c) 666 (d) 704
  5. 5.What is the 28th term of the AP 20, 22, 24, 26, …? (a) 74 (b) 56 (c) 76 (d) 54
  6. 6.Which term of the AP 19, 22, 25, 28, … is 88? (a) 24th (b) 26th (c) 23rd (d) 25th
  7. 7.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 104 (b) 96 (c) 192 (d) 19
  8. 8.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 256 (b) 232 (c) 50 (d) 464
  9. 9.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 22 (b) 14 (c) 15 (d) 16
  10. 10.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 812 (c) 406 (d) 378
  11. 11.What is the 11th term of the AP 17, 19, 21, 23, …? (a) 22 (b) 37 (c) 20 (d) 39
  12. 12.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 22 (b) 182 (c) 94 (d) 91
  13. 13.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 24 (c) 75 (d) 70
  14. 14.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 35 (b) 26 (c) 27 (d) 28
  15. 15.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 800 (c) 1640 (d) 820
  16. 16.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 252 (b) 36 (c) 144 (d) 126
  17. 17.What is the 31st term of the AP 18, 25, 32, 39, …? (a) 210 (b) 217 (c) 235 (d) 228
  18. 18.What is the 26th term of the AP 15, 21, 27, 33, …? (a) 156 (b) 150 (c) 165 (d) 171
  19. 19.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 350 (b) 59 (c) 320 (d) 640
  20. 20.What is the 12th term of the AP 18, 25, 32, 39, …? (a) 77 (b) 95 (c) 84 (d) 102
  21. 21.Which term of the AP 4, 7, 10, 13, … is 46? (a) 15th (b) 14th (c) 17th (d) 16th
  22. 22.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 429 (c) 69 (d) 462
  23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 45 (d) 276
  24. 24.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 4232 (c) 8556 (d) 4186
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  26. 26.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 374 (b) 341 (c) 61 (d) 682
  27. 27.What is the 24th term of the AP 16, 20, 24, 28, …? (a) 96 (b) 92 (c) 108 (d) 112
  28. 28.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 80 (c) 16 (d) 72
  29. 29.What is the 23rd term of the AP 4, 10, 16, 22, …? (a) 132 (b) 138 (c) 142 (d) 136
  30. 30.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 264 (b) 480 (c) 51 (d) 240
  31. 31.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 9312 (c) 4608 (d) 4656
  32. 32.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 40 (b) 360 (c) 200 (d) 180
  33. 33.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 242 (c) 506 (d) 253
  34. 34.Which term of the AP 6, 8, 10, 12, … is 84? (a) 39th (b) 40th (c) 41st (d) 42nd
  35. 35.What is the 21st term of the AP 18, 21, 24, 27, …? (a) 81 (b) 78 (c) 60 (d) 63
  36. 36.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 852 (b) 63 (c) 456 (d) 426
  37. 37.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 20 (b) 12 (c) 14 (d) 13
  38. 38.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1431 (c) 1458 (d) 1485
  39. 39.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 30 (c) 25 (d) 9
  40. 40.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 10 (c) 52 (d) 104

Answer key

  1. 225
  2. 57
  3. 35
  4. 703
  5. 74
  6. 24th
  7. 96
  8. 232
  9. 15
  10. 406
  11. 37
  12. 91
  13. 70
  14. 27
  15. 820
  16. 126
  17. 228
  18. 165
  19. 320
  20. 95
  21. 15th
  22. 429
  23. 529
  24. 4278
  25. 100
  26. 341
  27. 108
  28. 72
  29. 136
  30. 240
  31. 4656
  32. 180
  33. 253
  34. 40th
  35. 78
  36. 426
  37. 13
  38. 1485
  39. 25
  40. 52

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