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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 395 · 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 38th term of the AP 20, 25, 30, 35, …? (a) 210 (b) 185 (c) 190 (d) 205
  2. 2.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 4656 (d) 9312
  3. 3.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 60 (b) 110 (c) 55 (d) 21
  4. 4.What is the 29th term of the AP 9, 14, 19, 24, …? (a) 149 (b) 140 (c) 145 (d) 154
  5. 5.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 528 (b) 44 (c) 286 (d) 264
  6. 6.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 1332 (c) 648 (d) 630
  7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 153 (d) 306
  8. 8.Which term of the AP 4, 13, 22, 31, … is 202? (a) 24th (b) 22nd (c) 25th (d) 23rd
  9. 9.Which term of the AP 11, 20, 29, 38, … is 173? (a) 20th (b) 18th (c) 21st (d) 19th
  10. 10.What is the missing term in the AP 18, 26, ?, 42, 50? (a) 42 (b) 35 (c) 34 (d) 33
  11. 11.Which term of the AP 13, 15, 17, 19, … is 47? (a) 18th (b) 20th (c) 17th (d) 19th
  12. 12.What is the 32nd term of the AP 5, 10, 15, 20, …? (a) 161 (b) 160 (c) 165 (d) 155
  13. 13.What is the 10th term of the AP 10, 18, 26, 34, …? (a) 72 (b) 82 (c) 90 (d) 80
  14. 14.What is the 39th term of the AP 5, 10, 15, 20, …? (a) 190 (b) 195 (c) 196 (d) 200
  15. 15.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 224 (b) 119 (c) 22 (d) 112
  16. 16.What is the 24th term of the AP 1, 4, 7, 10, …? (a) 73 (b) 69 (c) 72 (d) 70
  17. 17.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 182 (c) 78 (d) 92
  18. 18.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 440 (b) 40 (c) 240 (d) 220
  19. 19.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 108 (c) 14 (d) 102
  20. 20.What is the 15th term of the AP 2, 5, 8, 11, …? (a) 47 (b) 45 (c) 42 (d) 44
  21. 21.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 330 (b) 25 (c) 165 (d) 176
  22. 22.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 36 (b) 252 (c) 234 (d) 468
  23. 23.What is the 11th term of the AP 4, 6, 8, 10, …? (a) 26 (b) 20 (c) 22 (d) 24
  24. 24.What is the 40th term of the AP 20, 23, 26, 29, …? (a) 117 (b) 137 (c) 120 (d) 140
  25. 25.What is the 31st term of the AP 18, 22, 26, 30, …? (a) 120 (b) 142 (c) 138 (d) 124
  26. 26.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 6 (b) 7 (c) 4 (d) 5
  27. 27.What is the sum of the first 11 terms of the AP 10, 16, 22, …? (a) 70 (b) 880 (c) 473 (d) 440
  28. 28.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 19 (b) 20 (c) 21 (d) 22
  29. 29.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 29 (b) 35 (c) 27 (d) 28
  30. 30.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 21 (b) 20 (c) 22 (d) 26
  31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 81 (d) 90
  32. 32.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 6 (b) 11 (c) 5 (d) 7
  33. 33.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 9 (b) 10 (c) 14 (d) 8
  34. 34.What is the 23rd term of the AP 19, 23, 27, 31, …? (a) 88 (b) 92 (c) 107 (d) 111
  35. 35.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 41 (b) 253 (c) 231 (d) 462
  36. 36.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 2415 (c) 4970 (d) 2450
  37. 37.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 300 (b) 324 (c) 47 (d) 600
  38. 38.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 676 (d) 351
  39. 39.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 203 (b) 182 (c) 44 (d) 364
  40. 40.Which term of the AP 8, 11, 14, 17, … is 77? (a) 24th (b) 23rd (c) 25th (d) 26th

Answer key

  1. 205
  2. 4656
  3. 55
  4. 149
  5. 264
  6. 666
  7. 289
  8. 23rd
  9. 19th
  10. 34
  11. 18th
  12. 160
  13. 82
  14. 195
  15. 112
  16. 70
  17. 91
  18. 220
  19. 102
  20. 44
  21. 165
  22. 234
  23. 24
  24. 137
  25. 138
  26. 5
  27. 440
  28. 20
  29. 28
  30. 21
  31. 81
  32. 6
  33. 9
  34. 107
  35. 231
  36. 2485
  37. 300
  38. 676
  39. 182
  40. 24th

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