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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 679 · 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 10th term of the AP 1, 9, 17, 25, …? (a) 73 (b) 72 (c) 81 (d) 80
  2. 2.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4851 (c) 4753 (d) 4802
  3. 3.What is the 40th term of the AP 7, 13, 19, 25, …? (a) 247 (b) 240 (c) 234 (d) 241
  4. 4.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1036 (c) 1035 (d) 2070
  5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 41 (d) 231
  6. 6.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 47 (d) 576
  7. 7.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 29 (b) 220 (c) 209 (d) 418
  8. 8.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 960 (b) 516 (c) 73 (d) 480
  9. 9.What is the 26th term of the AP 16, 22, 28, 34, …? (a) 172 (b) 156 (c) 166 (d) 150
  10. 10.What is the 10th term of the AP 11, 13, 15, 17, …? (a) 20 (b) 18 (c) 29 (d) 31
  11. 11.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 14 (b) 198 (c) 99 (d) 100
  12. 12.What is the sum of all the whole numbers from 1 to 79? (a) 6320 (b) 3160 (c) 3161 (d) 3081
  13. 13.What is the 23rd term of the AP 1, 3, 5, 7, …? (a) 45 (b) 44 (c) 47 (d) 46
  14. 14.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 66 (b) 132 (c) 21 (d) 78
  15. 15.What is the 28th term of the AP 10, 19, 28, 37, …? (a) 253 (b) 243 (c) 262 (d) 252
  16. 16.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3240 (c) 3160 (d) 3200
  17. 17.What is the missing term in the AP 16, 22, ?, 34, 40? (a) 29 (b) 34 (c) 28 (d) 27
  18. 18.What is the 31st term of the AP 7, 14, 21, 28, …? (a) 218 (b) 210 (c) 224 (d) 217
  19. 19.What is the 19th term of the AP 7, 12, 17, 22, …? (a) 90 (b) 95 (c) 97 (d) 102
  20. 20.What is the 22nd term of the AP 2, 9, 16, 23, …? (a) 154 (b) 156 (c) 147 (d) 149
  21. 21.Which term of the AP 18, 20, 22, 24, … is 96? (a) 39th (b) 40th (c) 41st (d) 48th
  22. 22.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 666 (c) 630 (d) 1332
  23. 23.What is the 40th term of the AP 9, 12, 15, 18, …? (a) 120 (b) 117 (c) 129 (d) 126
  24. 24.What is the 12th term of the AP 6, 8, 10, 12, …? (a) 30 (b) 28 (c) 24 (d) 22
  25. 25.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 456 (b) 426 (c) 852 (d) 63
  26. 26.What is the 33rd term of the AP 20, 26, 32, 38, …? (a) 192 (b) 212 (c) 218 (d) 198
  27. 27.What is the 12th term of the AP 13, 18, 23, 28, …? (a) 55 (b) 73 (c) 60 (d) 68
  28. 28.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 39 (b) 30 (c) 32 (d) 31
  29. 29.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 20 (b) 23 (c) 18 (d) 19
  30. 30.What is the 15th term of the AP 15, 21, 27, 33, …? (a) 105 (b) 90 (c) 99 (d) 84
  31. 31.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 33 (b) 198 (c) 396 (d) 201
  32. 32.What is the 30th term of the AP 16, 22, 28, 34, …? (a) 190 (b) 180 (c) 196 (d) 174
  33. 33.What is the 14th term of the AP 11, 20, 29, 38, …? (a) 117 (b) 137 (c) 128 (d) 126
  34. 34.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 400 (b) 38 (c) 220 (d) 200
  35. 35.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 240 (b) 30 (c) 132 (d) 120
  36. 36.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 552 (b) 76 (c) 516 (d) 1032
  37. 37.What is the 19th term of the AP 12, 15, 18, 21, …? (a) 66 (b) 57 (c) 54 (d) 69
  38. 38.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 22 (b) 24 (c) 31 (d) 23
  39. 39.What is the 12th term of the AP 4, 6, 8, 10, …? (a) 26 (b) 22 (c) 28 (d) 24
  40. 40.What is the 18th term of the AP 7, 9, 11, 13, …? (a) 36 (b) 34 (c) 43 (d) 41

Answer key

  1. 73
  2. 4851
  3. 241
  4. 1035
  5. 441
  6. 576
  7. 209
  8. 480
  9. 166
  10. 29
  11. 99
  12. 3160
  13. 45
  14. 66
  15. 253
  16. 3240
  17. 28
  18. 217
  19. 97
  20. 149
  21. 40th
  22. 666
  23. 126
  24. 28
  25. 426
  26. 212
  27. 68
  28. 31
  29. 19
  30. 99
  31. 198
  32. 190
  33. 128
  34. 200
  35. 120
  36. 516
  37. 66
  38. 23
  39. 26
  40. 41

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