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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 408 · 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.Which term of the AP 15, 20, 25, 30, … is 75? (a) 12th (b) 15th (c) 14th (d) 13th
  2. 2.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 312 (b) 576 (c) 46 (d) 288
  3. 3.What is the 25th term of the AP 20, 22, 24, 26, …? (a) 70 (b) 68 (c) 50 (d) 48
  4. 4.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 90 (b) 96 (c) 13 (d) 180
  5. 5.What is the 38th term of the AP 6, 8, 10, 12, …? (a) 82 (b) 76 (c) 80 (d) 74
  6. 6.What is the 24th term of the AP 16, 22, 28, 34, …? (a) 144 (b) 160 (c) 138 (d) 154
  7. 7.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 280 (b) 520 (c) 44 (d) 260
  8. 8.What is the 26th term of the AP 5, 7, 9, 11, …? (a) 55 (b) 57 (c) 50 (d) 52
  9. 9.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 1800 (c) 1830 (d) 3660
  10. 10.What is the missing term in the AP 18, 27, ?, 45, 54? (a) 35 (b) 45 (c) 36 (d) 37
  11. 11.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 24 (b) 154 (c) 308 (d) 165
  12. 12.What is the 20th term of the AP 16, 20, 24, 28, …? (a) 76 (b) 80 (c) 92 (d) 96
  13. 13.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 90 (b) 27 (c) 150 (d) 75
  14. 14.Which term of the AP 11, 15, 19, 23, … is 63? (a) 13th (b) 16th (c) 14th (d) 15th
  15. 15.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 729 (d) 53
  16. 16.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 12 (c) 60 (d) 57
  17. 17.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 248 (b) 26 (c) 136 (d) 124
  18. 18.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 30 (b) 31 (c) 60 (d) 8
  19. 19.What is the 30th term of the AP 8, 10, 12, 14, …? (a) 60 (b) 68 (c) 58 (d) 66
  20. 20.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 4005 (c) 3916 (d) 8010
  21. 21.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 15 (b) 21 (c) 13 (d) 14
  22. 22.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 78 (b) 21 (c) 75 (d) 150
  23. 23.What is the 29th term of the AP 3, 9, 15, 21, …? (a) 174 (b) 171 (c) 177 (d) 168
  24. 24.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 5 (b) 15 (c) 16 (d) 30
  25. 25.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 2556 (c) 2628 (d) 5256
  26. 26.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 51 (b) 102 (c) 60 (d) 16
  27. 27.What is the 23rd term of the AP 6, 8, 10, 12, …? (a) 46 (b) 52 (c) 50 (d) 44
  28. 28.What is the 17th term of the AP 9, 12, 15, 18, …? (a) 57 (b) 51 (c) 60 (d) 48
  29. 29.Which term of the AP 8, 17, 26, 35, … is 125? (a) 13th (b) 15th (c) 14th (d) 16th
  30. 30.What is the 25th term of the AP 18, 21, 24, 27, …? (a) 93 (b) 72 (c) 75 (d) 90
  31. 31.What is the 40th term of the AP 8, 13, 18, 23, …? (a) 208 (b) 195 (c) 203 (d) 200
  32. 32.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 109 (b) 216 (c) 108 (d) 16
  33. 33.What is the 27th term of the AP 14, 22, 30, 38, …? (a) 222 (b) 230 (c) 216 (d) 208
  34. 34.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1458 (c) 1431 (d) 1485
  35. 35.What is the 27th term of the AP 6, 14, 22, 30, …? (a) 216 (b) 214 (c) 222 (d) 208
  36. 36.What is the missing term in the AP 4, 13, 22, ?, 40? (a) 30 (b) 32 (c) 40 (d) 31
  37. 37.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 90 (b) 80 (c) 24 (d) 160
  38. 38.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 5700 (c) 2850 (d) 2851
  39. 39.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 12 (b) 13 (c) 14 (d) 18
  40. 40.Which term of the AP 3, 6, 9, 12, … is 72? (a) 26th (b) 23rd (c) 25th (d) 24th

Answer key

  1. 13th
  2. 288
  3. 68
  4. 90
  5. 80
  6. 154
  7. 260
  8. 55
  9. 1830
  10. 36
  11. 154
  12. 92
  13. 75
  14. 14th
  15. 729
  16. 57
  17. 124
  18. 30
  19. 66
  20. 4005
  21. 14
  22. 75
  23. 171
  24. 15
  25. 2628
  26. 51
  27. 50
  28. 57
  29. 14th
  30. 90
  31. 203
  32. 108
  33. 222
  34. 1485
  35. 214
  36. 31
  37. 80
  38. 2850
  39. 13
  40. 24th

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