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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 765 · 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 7 terms of the AP 6, 7, 8, …? (a) 63 (b) 64 (c) 126 (d) 12
  2. 2.What is the sum of all the whole numbers from 1 to 89? (a) 3916 (b) 4006 (c) 8010 (d) 4005
  3. 3.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 90 (b) 18 (c) 180 (d) 99
  4. 4.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1485 (c) 1431 (d) 1458
  5. 5.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 96 (b) 13 (c) 180 (d) 90
  6. 6.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 33 (b) 8 (c) 36 (d) 66
  7. 7.Which term of the AP 6, 15, 24, 33, … is 132? (a) 16th (b) 17th (c) 15th (d) 14th
  8. 8.What is the 33rd term of the AP 11, 19, 27, 35, …? (a) 264 (b) 275 (c) 267 (d) 256
  9. 9.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1081 (c) 1035 (d) 2162
  10. 10.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 1035 (c) 2070 (d) 990
  11. 11.What is the 15th term of the AP 8, 11, 14, 17, …? (a) 45 (b) 42 (c) 53 (d) 50
  12. 12.Which term of the AP 17, 22, 27, 32, … is 132? (a) 24th (b) 26th (c) 25th (d) 23rd
  13. 13.What is the 23rd term of the AP 3, 9, 15, 21, …? (a) 141 (b) 138 (c) 135 (d) 132
  14. 14.Which term of the AP 9, 13, 17, 21, … is 73? (a) 18th (b) 16th (c) 19th (d) 17th
  15. 15.What is the missing term in the AP 19, 26, 33, ?, 47? (a) 39 (b) 40 (c) 47 (d) 41
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 190 (d) 380
  17. 17.Which term of the AP 4, 11, 18, 25, … is 95? (a) 16th (b) 13th (c) 15th (d) 14th
  18. 18.Which term of the AP 8, 16, 24, 32, … is 216? (a) 26th (b) 28th (c) 29th (d) 27th
  19. 19.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3042 (d) 3081
  20. 20.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 6 (b) 8 (c) 4 (d) 5
  21. 21.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 15 (b) 85 (c) 84 (d) 168
  22. 22.What is the missing term in the AP 19, 26, ?, 40, 47? (a) 32 (b) 40 (c) 34 (d) 33
  23. 23.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 3 (c) 5 (d) 4
  24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
  25. 25.Which term of the AP 20, 22, 24, 26, … is 50? (a) 17th (b) 25th (c) 16th (d) 15th
  26. 26.What is the 12th term of the AP 10, 18, 26, 34, …? (a) 88 (b) 106 (c) 98 (d) 96
  27. 27.What is the 36th term of the AP 4, 10, 16, 22, …? (a) 214 (b) 216 (c) 210 (d) 220
  28. 28.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 77 (b) 17 (c) 84 (d) 154
  29. 29.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 10 (b) 9 (c) 13 (d) 8
  30. 30.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 48 (b) 40 (c) 39 (d) 41
  31. 31.What is the 20th term of the AP 17, 21, 25, 29, …? (a) 80 (b) 93 (c) 76 (d) 97
  32. 32.Which term of the AP 4, 12, 20, 28, … is 60? (a) 8th (b) 9th (c) 7th (d) 10th
  33. 33.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 11 (b) 15 (c) 12 (d) 13
  34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  35. 35.Which term of the AP 12, 15, 18, 21, … is 81? (a) 24th (b) 25th (c) 27th (d) 23rd
  36. 36.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 528 (b) 492 (c) 74 (d) 984
  37. 37.What is the 14th term of the AP 14, 19, 24, 29, …? (a) 70 (b) 84 (c) 65 (d) 79
  38. 38.What is the 14th term of the AP 17, 21, 25, 29, …? (a) 73 (b) 52 (c) 69 (d) 56
  39. 39.What is the 40th term of the AP 15, 21, 27, 33, …? (a) 255 (b) 249 (c) 234 (d) 240
  40. 40.What is the 21st term of the AP 3, 11, 19, 27, …? (a) 160 (b) 171 (c) 168 (d) 163

Answer key

  1. 63
  2. 4005
  3. 90
  4. 1485
  5. 90
  6. 33
  7. 15th
  8. 267
  9. 1081
  10. 1035
  11. 50
  12. 24th
  13. 135
  14. 17th
  15. 40
  16. 361
  17. 14th
  18. 27th
  19. 3081
  20. 5
  21. 84
  22. 33
  23. 4
  24. 676
  25. 16th
  26. 98
  27. 214
  28. 77
  29. 9
  30. 40
  31. 93
  32. 8th
  33. 12
  34. 729
  35. 24th
  36. 492
  37. 79
  38. 69
  39. 249
  40. 163

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