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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 323 · 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 9 terms of the AP 8, 12, 16, …? (a) 40 (b) 432 (c) 234 (d) 216
  2. 2.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 90 (b) 162 (c) 17 (d) 81
  3. 3.What is the 20th term of the AP 17, 24, 31, 38, …? (a) 150 (b) 133 (c) 140 (d) 157
  4. 4.What is the missing term in the AP 19, 26, 33, ?, 47? (a) 41 (b) 47 (c) 39 (d) 40
  5. 5.Which term of the AP 14, 17, 20, 23, … is 50? (a) 12th (b) 13th (c) 15th (d) 14th
  6. 6.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 35 (d) 342
  7. 7.What is the 14th term of the AP 7, 13, 19, 25, …? (a) 91 (b) 84 (c) 85 (d) 78
  8. 8.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 150 (b) 27 (c) 75 (d) 90
  9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 110 (d) 55
  10. 10.What is the missing term in the AP 2, 10, 18, ?, 34? (a) 25 (b) 26 (c) 27 (d) 34
  11. 11.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 5112 (c) 2556 (d) 2485
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 812 (d) 784
  13. 13.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 10 (b) 11 (c) 9 (d) 13
  14. 14.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4851 (c) 9900 (d) 4950
  15. 15.What is the missing term in the AP 11, 13, 15, ?, 19? (a) 17 (b) 16 (c) 18 (d) 19
  16. 16.What is the 40th term of the AP 19, 21, 23, 25, …? (a) 97 (b) 80 (c) 78 (d) 99
  17. 17.What is the 35th term of the AP 1, 9, 17, 25, …? (a) 281 (b) 272 (c) 273 (d) 280
  18. 18.What is the 15th term of the AP 11, 13, 15, 17, …? (a) 41 (b) 39 (c) 28 (d) 30
  19. 19.What is the 21st term of the AP 13, 19, 25, 31, …? (a) 120 (b) 126 (c) 133 (d) 139
  20. 20.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 21 (b) 22 (c) 23 (d) 27
  21. 21.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 9702 (c) 4851 (d) 4802
  22. 22.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 200 (d) 190
  23. 23.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  24. 24.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 120 (b) 65 (c) 60 (d) 22
  25. 25.What is the missing term in the AP 19, 22, 25, ?, 31? (a) 28 (b) 27 (c) 29 (d) 31
  26. 26.What is the 17th term of the AP 3, 5, 7, 9, …? (a) 32 (b) 34 (c) 37 (d) 35
  27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 21 (d) 11
  28. 28.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 351 (d) 702
  29. 29.Which term of the AP 20, 29, 38, 47, … is 299? (a) 33rd (b) 31st (c) 34th (d) 32nd
  30. 30.What is the 19th term of the AP 5, 12, 19, 26, …? (a) 131 (b) 126 (c) 133 (d) 138
  31. 31.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 21 (b) 19 (c) 20 (d) 27
  32. 32.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 121 (b) 132 (c) 242 (d) 21
  33. 33.What is the 15th term of the AP 14, 17, 20, 23, …? (a) 42 (b) 45 (c) 56 (d) 59
  34. 34.Which term of the AP 16, 21, 26, 31, … is 121? (a) 23rd (b) 22nd (c) 21st (d) 24th
  35. 35.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 120 (c) 272 (d) 136
  36. 36.What is the 37th term of the AP 4, 9, 14, 19, …? (a) 185 (b) 184 (c) 180 (d) 189
  37. 37.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 59 (c) 930 (d) 465
  38. 38.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 108 (b) 198 (c) 19 (d) 99
  39. 39.Which term of the AP 17, 19, 21, 23, … is 89? (a) 39th (b) 37th (c) 36th (d) 38th
  40. 40.What is the 34th term of the AP 2, 7, 12, 17, …? (a) 172 (b) 165 (c) 167 (d) 170

Answer key

  1. 216
  2. 81
  3. 150
  4. 40
  5. 13th
  6. 324
  7. 85
  8. 75
  9. 100
  10. 26
  11. 2556
  12. 784
  13. 10
  14. 4950
  15. 17
  16. 97
  17. 273
  18. 39
  19. 133
  20. 22
  21. 4851
  22. 210
  23. 144
  24. 60
  25. 28
  26. 35
  27. 36
  28. 351
  29. 32nd
  30. 131
  31. 20
  32. 121
  33. 56
  34. 22nd
  35. 136
  36. 184
  37. 900
  38. 99
  39. 37th
  40. 167

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