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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 886 · 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 all the whole numbers from 1 to 31? (a) 497 (b) 465 (c) 992 (d) 496
  2. 2.What is the 12th term of the AP 1, 9, 17, 25, …? (a) 88 (b) 96 (c) 97 (d) 89
  3. 3.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 2550 (c) 1275 (d) 1225
  4. 4.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 266 (b) 49 (c) 261 (d) 522
  5. 5.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 462 (b) 36 (c) 231 (d) 234
  6. 6.What is the 18th term of the AP 6, 9, 12, 15, …? (a) 51 (b) 54 (c) 57 (d) 60
  7. 7.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 34 (b) 198 (c) 396 (d) 201
  8. 8.Which term of the AP 5, 7, 9, 11, … is 27? (a) 12th (b) 11th (c) 13th (d) 14th
  9. 9.What is the 31st term of the AP 16, 22, 28, 34, …? (a) 180 (b) 202 (c) 186 (d) 196
  10. 10.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 180 (b) 13 (c) 96 (d) 90
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 506 (c) 484 (d) 43
  12. 12.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 5000 (d) 10100
  13. 13.What is the 16th term of the AP 6, 15, 24, 33, …? (a) 141 (b) 144 (c) 135 (d) 150
  14. 14.What is the 32nd term of the AP 15, 21, 27, 33, …? (a) 207 (b) 201 (c) 186 (d) 192
  15. 15.What is the 32nd term of the AP 13, 19, 25, 31, …? (a) 192 (b) 186 (c) 199 (d) 205
  16. 16.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 26 (b) 85 (c) 80 (d) 160
  17. 17.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 29 (b) 23 (c) 24 (d) 25
  18. 18.What is the 10th term of the AP 7, 14, 21, 28, …? (a) 70 (b) 71 (c) 63 (d) 77
  19. 19.What is the 39th term of the AP 12, 20, 28, 36, …? (a) 324 (b) 304 (c) 312 (d) 316
  20. 20.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 44 (b) 36 (c) 34 (d) 35
  21. 21.What is the 14th term of the AP 14, 17, 20, 23, …? (a) 42 (b) 53 (c) 56 (d) 39
  22. 22.What is the 26th term of the AP 20, 24, 28, 32, …? (a) 100 (b) 124 (c) 120 (d) 104
  23. 23.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 192 (b) 19 (c) 104 (d) 96
  24. 24.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 23 (b) 29 (c) 22 (d) 24
  25. 25.What is the 15th term of the AP 2, 6, 10, 14, …? (a) 62 (b) 60 (c) 56 (d) 58
  26. 26.What is the 18th term of the AP 5, 13, 21, 29, …? (a) 141 (b) 144 (c) 149 (d) 136
  27. 27.What is the 30th term of the AP 5, 8, 11, 14, …? (a) 95 (b) 90 (c) 92 (d) 87
  28. 28.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 51 (c) 12 (d) 50
  29. 29.What is the 14th term of the AP 10, 19, 28, 37, …? (a) 126 (b) 117 (c) 136 (d) 127
  30. 30.Which term of the AP 3, 6, 9, 12, … is 66? (a) 21st (b) 24th (c) 23rd (d) 22nd
  31. 31.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 4 (b) 5 (c) 6 (d) 7
  32. 32.What is the 21st term of the AP 10, 17, 24, 31, …? (a) 150 (b) 140 (c) 147 (d) 157
  33. 33.What is the 36th term of the AP 2, 8, 14, 20, …? (a) 210 (b) 212 (c) 218 (d) 216
  34. 34.Which term of the AP 11, 18, 25, 32, … is 151? (a) 20th (b) 22nd (c) 21st (d) 23rd
  35. 35.What is the 19th term of the AP 13, 22, 31, 40, …? (a) 175 (b) 171 (c) 184 (d) 162
  36. 36.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 222 (b) 240 (c) 35 (d) 444
  37. 37.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 325 (c) 326 (d) 300
  38. 38.What is the 21st term of the AP 19, 28, 37, 46, …? (a) 180 (b) 208 (c) 189 (d) 199
  39. 39.Which term of the AP 20, 26, 32, 38, … is 254? (a) 40th (b) 42nd (c) 39th (d) 41st
  40. 40.What is the 23rd term of the AP 17, 19, 21, 23, …? (a) 63 (b) 44 (c) 61 (d) 46

Answer key

  1. 496
  2. 89
  3. 1275
  4. 261
  5. 231
  6. 57
  7. 198
  8. 12th
  9. 196
  10. 90
  11. 484
  12. 5050
  13. 141
  14. 201
  15. 199
  16. 80
  17. 24
  18. 70
  19. 316
  20. 35
  21. 53
  22. 120
  23. 96
  24. 23
  25. 58
  26. 141
  27. 92
  28. 50
  29. 127
  30. 22nd
  31. 5
  32. 150
  33. 212
  34. 21st
  35. 175
  36. 222
  37. 325
  38. 199
  39. 40th
  40. 61

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