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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 535 · 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 27th term of the AP 6, 13, 20, 27, …? (a) 189 (b) 188 (c) 195 (d) 182
  2. 2.What is the 19th term of the AP 14, 22, 30, 38, …? (a) 166 (b) 144 (c) 152 (d) 158
  3. 3.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 110 (b) 55 (c) 21 (d) 60
  4. 4.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 128 (b) 15 (c) 72 (d) 64
  5. 5.What is the sum of all the whole numbers from 1 to 88? (a) 3916 (b) 3872 (c) 3828 (d) 7832
  6. 6.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 18 (b) 19 (c) 23 (d) 17
  7. 7.What is the 36th term of the AP 9, 17, 25, 33, …? (a) 289 (b) 280 (c) 297 (d) 288
  8. 8.What is the 32nd term of the AP 17, 26, 35, 44, …? (a) 288 (b) 305 (c) 296 (d) 279
  9. 9.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 196 (b) 98 (c) 105 (d) 20
  10. 10.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 162 (c) 153 (d) 342
  11. 11.Which term of the AP 9, 13, 17, 21, … is 89? (a) 20th (b) 22nd (c) 23rd (d) 21st
  12. 12.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 396 (b) 63 (c) 726 (d) 363
  13. 13.What is the 32nd term of the AP 6, 10, 14, 18, …? (a) 134 (b) 124 (c) 130 (d) 128
  14. 14.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 25 (b) 17 (c) 18 (d) 19
  15. 15.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 59 (b) 378 (c) 756 (d) 408
  16. 16.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 6 (c) 21 (d) 40
  17. 17.What is the 25th term of the AP 11, 13, 15, 17, …? (a) 59 (b) 61 (c) 48 (d) 50
  18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
  19. 19.What is the 18th term of the AP 1, 10, 19, 28, …? (a) 153 (b) 163 (c) 154 (d) 162
  20. 20.Which term of the AP 3, 8, 13, 18, … is 38? (a) 9th (b) 8th (c) 7th (d) 10th
  21. 21.Which term of the AP 11, 17, 23, 29, … is 125? (a) 19th (b) 20th (c) 21st (d) 22nd
  22. 22.What is the 25th term of the AP 5, 10, 15, 20, …? (a) 125 (b) 126 (c) 120 (d) 130
  23. 23.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 21 (b) 117 (c) 126 (d) 234
  24. 24.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 180 (b) 165 (c) 30 (d) 330
  25. 25.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 17 (b) 16 (c) 15 (d) 25
  26. 26.Which term of the AP 5, 10, 15, 20, … is 70? (a) 13th (b) 14th (c) 15th (d) 16th
  27. 27.What is the 37th term of the AP 15, 19, 23, 27, …? (a) 159 (b) 144 (c) 148 (d) 163
  28. 28.Which term of the AP 1, 7, 13, 19, … is 127? (a) 21st (b) 23rd (c) 22nd (d) 24th
  29. 29.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 54 (b) 768 (c) 408 (d) 384
  30. 30.Which term of the AP 1, 4, 7, 10, … is 97? (a) 33rd (b) 32nd (c) 34th (d) 35th
  31. 31.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 13 (b) 56 (c) 110 (d) 55
  32. 32.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 530 (b) 265 (c) 290 (d) 49
  33. 33.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 7 (b) 13 (c) 9 (d) 8
  34. 34.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 280 (b) 46 (c) 560 (d) 300
  35. 35.What is the 14th term of the AP 4, 9, 14, 19, …? (a) 74 (b) 70 (c) 69 (d) 65
  36. 36.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 60 (b) 18 (c) 120 (d) 63
  37. 37.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4851 (c) 4950 (d) 4951
  38. 38.What is the 39th term of the AP 2, 4, 6, 8, …? (a) 78 (b) 79 (c) 80 (d) 76
  39. 39.Which term of the AP 6, 11, 16, 21, … is 116? (a) 22nd (b) 24th (c) 23rd (d) 25th
  40. 40.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 41 (d) 441

Answer key

  1. 188
  2. 158
  3. 55
  4. 64
  5. 3916
  6. 18
  7. 289
  8. 296
  9. 98
  10. 171
  11. 21st
  12. 363
  13. 130
  14. 18
  15. 378
  16. 20
  17. 59
  18. 81
  19. 154
  20. 8th
  21. 20th
  22. 125
  23. 117
  24. 165
  25. 16
  26. 14th
  27. 159
  28. 22nd
  29. 384
  30. 33rd
  31. 55
  32. 265
  33. 8
  34. 280
  35. 69
  36. 60
  37. 4950
  38. 78
  39. 23rd
  40. 441

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