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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 162 · 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 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
  2. 2.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 198 (b) 201 (c) 396 (d) 34
  3. 3.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 576 (d) 300
  4. 4.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 108 (b) 14 (c) 102 (d) 204
  5. 5.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 8 (b) 6 (c) 7 (d) 13
  6. 6.Which term of the AP 16, 18, 20, 22, … is 42? (a) 13th (b) 15th (c) 14th (d) 21st
  7. 7.What is the 39th term of the AP 9, 16, 23, 30, …? (a) 273 (b) 275 (c) 266 (d) 282
  8. 8.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 108 (b) 55 (c) 54 (d) 10
  9. 9.What is the 11th term of the AP 20, 28, 36, 44, …? (a) 100 (b) 88 (c) 108 (d) 80
  10. 10.Which term of the AP 7, 16, 25, 34, … is 295? (a) 32nd (b) 35th (c) 33rd (d) 34th
  11. 11.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 15 (b) 14 (c) 16 (d) 13
  12. 12.What is the 12th term of the AP 20, 23, 26, 29, …? (a) 53 (b) 56 (c) 33 (d) 36
  13. 13.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 19 (b) 18 (c) 17 (d) 21
  14. 14.What is the 12th term of the AP 9, 14, 19, 24, …? (a) 60 (b) 64 (c) 55 (d) 69
  15. 15.What is the 38th term of the AP 14, 17, 20, 23, …? (a) 128 (b) 114 (c) 125 (d) 111
  16. 16.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 10 (c) 55 (d) 60
  17. 17.What is the 33rd term of the AP 10, 18, 26, 34, …? (a) 256 (b) 266 (c) 264 (d) 274
  18. 18.Which term of the AP 19, 23, 27, 31, … is 155? (a) 36th (b) 34th (c) 35th (d) 37th
  19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  20. 20.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 25 (c) 130 (d) 65
  21. 21.What is the 22nd term of the AP 17, 23, 29, 35, …? (a) 143 (b) 132 (c) 149 (d) 126
  22. 22.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 600 (c) 276 (d) 300
  23. 23.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
  24. 24.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 27 (b) 30 (c) 54 (d) 7
  25. 25.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 114 (b) 228 (c) 132 (d) 34
  26. 26.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 12 (b) 80 (c) 40 (d) 45
  27. 27.What is the missing term in the AP 19, 21, 23, ?, 27? (a) 25 (b) 24 (c) 26 (d) 27
  28. 28.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2346 (c) 4830 (d) 2416
  29. 29.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  30. 30.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 1225 (c) 2550 (d) 1275
  31. 31.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 23 (b) 144 (c) 156 (d) 288
  32. 32.What is the 13th term of the AP 6, 9, 12, 15, …? (a) 45 (b) 39 (c) 42 (d) 36
  33. 33.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 42 (b) 612 (c) 306 (d) 324
  34. 34.What is the 12th term of the AP 4, 7, 10, 13, …? (a) 33 (b) 40 (c) 37 (d) 36
  35. 35.Which term of the AP 12, 21, 30, 39, … is 156? (a) 17th (b) 18th (c) 19th (d) 16th
  36. 36.What is the 26th term of the AP 8, 11, 14, 17, …? (a) 75 (b) 86 (c) 78 (d) 83
  37. 37.Which term of the AP 13, 18, 23, 28, … is 103? (a) 21st (b) 20th (c) 19th (d) 18th
  38. 38.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 2851 (c) 2775 (d) 5700
  39. 39.What is the 19th term of the AP 10, 12, 14, 16, …? (a) 46 (b) 48 (c) 38 (d) 36
  40. 40.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 184 (b) 164 (c) 328 (d) 38

Answer key

  1. 324
  2. 198
  3. 576
  4. 102
  5. 7
  6. 14th
  7. 275
  8. 54
  9. 100
  10. 33rd
  11. 14
  12. 53
  13. 18
  14. 64
  15. 125
  16. 55
  17. 266
  18. 35th
  19. 100
  20. 65
  21. 143
  22. 300
  23. 529
  24. 27
  25. 114
  26. 40
  27. 25
  28. 2415
  29. 841
  30. 1275
  31. 144
  32. 42
  33. 306
  34. 37
  35. 17th
  36. 83
  37. 19th
  38. 2850
  39. 46
  40. 164

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