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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 779 · 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 89? (a) 8010 (b) 3916 (c) 4005 (d) 4006
  2. 2.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 41 (b) 36 (c) 35 (d) 34
  3. 3.What is the 15th term of the AP 18, 23, 28, 33, …? (a) 93 (b) 88 (c) 70 (d) 75
  4. 4.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 21 (b) 16 (c) 17 (d) 15
  5. 5.What is the 36th term of the AP 12, 20, 28, 36, …? (a) 288 (b) 280 (c) 292 (d) 300
  6. 6.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 5112 (c) 2557 (d) 2485
  7. 7.Which term of the AP 1, 4, 7, 10, … is 97? (a) 33rd (b) 32nd (c) 34th (d) 35th
  8. 8.What is the 34th term of the AP 18, 25, 32, 39, …? (a) 238 (b) 249 (c) 256 (d) 231
  9. 9.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 960 (b) 73 (c) 516 (d) 480
  10. 10.Which term of the AP 19, 23, 27, 31, … is 139? (a) 30th (b) 32nd (c) 33rd (d) 31st
  11. 11.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 612 (c) 324 (d) 42
  12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
  13. 13.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 31 (b) 24 (c) 25 (d) 23
  14. 14.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 92 (d) 91
  15. 15.What is the sum of all the whole numbers from 1 to 83? (a) 3486 (b) 3403 (c) 6972 (d) 3487
  16. 16.What is the 21st term of the AP 13, 21, 29, 37, …? (a) 160 (b) 181 (c) 173 (d) 168
  17. 17.Which term of the AP 5, 9, 13, 17, … is 61? (a) 15th (b) 14th (c) 17th (d) 16th
  18. 18.What is the 35th term of the AP 20, 23, 26, 29, …? (a) 122 (b) 102 (c) 125 (d) 105
  19. 19.What is the 21st term of the AP 1, 3, 5, 7, …? (a) 42 (b) 40 (c) 41 (d) 43
  20. 20.What is the 26th term of the AP 6, 11, 16, 21, …? (a) 136 (b) 130 (c) 131 (d) 125
  21. 21.Which term of the AP 12, 18, 24, 30, … is 60? (a) 9th (b) 10th (c) 8th (d) 11th
  22. 22.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 360 (b) 672 (c) 336 (d) 50
  23. 23.What is the 10th term of the AP 15, 21, 27, 33, …? (a) 69 (b) 75 (c) 54 (d) 60
  24. 24.Which term of the AP 16, 24, 32, 40, … is 160? (a) 18th (b) 20th (c) 19th (d) 21st
  25. 25.What is the 27th term of the AP 20, 26, 32, 38, …? (a) 176 (b) 156 (c) 162 (d) 182
  26. 26.What is the 11th term of the AP 1, 4, 7, 10, …? (a) 34 (b) 33 (c) 31 (d) 30
  27. 27.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 351 (c) 325 (d) 338
  28. 28.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 192 (b) 21 (c) 186 (d) 372
  29. 29.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  30. 30.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 11 (b) 13 (c) 14 (d) 12
  31. 31.What is the 39th term of the AP 13, 16, 19, 22, …? (a) 117 (b) 114 (c) 130 (d) 127
  32. 32.What is the sum of all the whole numbers from 1 to 87? (a) 7656 (b) 3741 (c) 3828 (d) 3829
  33. 33.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 41 (b) 32 (c) 31 (d) 33
  34. 34.What is the 25th term of the AP 8, 13, 18, 23, …? (a) 133 (b) 125 (c) 120 (d) 128
  35. 35.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 87 (b) 22 (c) 96 (d) 174
  36. 36.What is the 32nd term of the AP 16, 25, 34, 43, …? (a) 288 (b) 295 (c) 279 (d) 304
  37. 37.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 43 (c) 40 (d) 80
  38. 38.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 516 (b) 276 (c) 258 (d) 38
  39. 39.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 37 (b) 31 (c) 29 (d) 30
  40. 40.What is the 33rd term of the AP 5, 10, 15, 20, …? (a) 166 (b) 165 (c) 170 (d) 160

Answer key

  1. 4005
  2. 35
  3. 88
  4. 16
  5. 292
  6. 2556
  7. 33rd
  8. 249
  9. 480
  10. 31st
  11. 306
  12. 121
  13. 24
  14. 91
  15. 3486
  16. 173
  17. 15th
  18. 122
  19. 41
  20. 131
  21. 9th
  22. 336
  23. 69
  24. 19th
  25. 176
  26. 31
  27. 351
  28. 186
  29. 441
  30. 12
  31. 127
  32. 3828
  33. 32
  34. 128
  35. 87
  36. 295
  37. 40
  38. 258
  39. 30
  40. 165

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