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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 676 · 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 11th term of the AP 11, 19, 27, 35, …? (a) 80 (b) 91 (c) 88 (d) 99
  2. 2.What is the missing term in the AP 12, 20, 28, ?, 44? (a) 35 (b) 37 (c) 36 (d) 44
  3. 3.Which term of the AP 3, 5, 7, 9, … is 21? (a) 12th (b) 9th (c) 11th (d) 10th
  4. 4.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  5. 5.What is the missing term in the AP 20, ?, 30, 35, 40? (a) 24 (b) 25 (c) 26 (d) 30
  6. 6.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100
  7. 7.What is the 17th term of the AP 11, 19, 27, 35, …? (a) 147 (b) 136 (c) 139 (d) 128
  8. 8.What is the 25th term of the AP 6, 8, 10, 12, …? (a) 48 (b) 50 (c) 54 (d) 56
  9. 9.What is the 37th term of the AP 3, 10, 17, 24, …? (a) 252 (b) 259 (c) 255 (d) 262
  10. 10.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 66 (d) 67
  11. 11.Which term of the AP 16, 25, 34, 43, … is 178? (a) 20th (b) 19th (c) 21st (d) 18th
  12. 12.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1432 (c) 2862 (d) 1431
  13. 13.What is the missing term in the AP 13, 21, 29, ?, 45? (a) 38 (b) 45 (c) 37 (d) 36
  14. 14.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 78 (d) 156
  15. 15.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4851 (c) 4951 (d) 4950
  16. 16.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 17 (b) 130 (c) 125 (d) 250
  17. 17.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 171 (b) 174 (c) 342 (d) 31
  18. 18.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 23 (b) 22 (c) 25 (d) 21
  19. 19.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 18 (b) 21 (c) 17 (d) 19
  20. 20.Which term of the AP 19, 26, 33, 40, … is 159? (a) 20th (b) 22nd (c) 23rd (d) 21st
  21. 21.What is the 34th term of the AP 10, 16, 22, 28, …? (a) 198 (b) 204 (c) 214 (d) 208
  22. 22.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1892 (c) 1830 (d) 1891
  23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 576 (d) 600
  24. 24.What is the 29th term of the AP 15, 18, 21, 24, …? (a) 99 (b) 84 (c) 87 (d) 102
  25. 25.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 418 (b) 451 (c) 836 (d) 68
  26. 26.What is the 16th term of the AP 17, 19, 21, 23, …? (a) 49 (b) 47 (c) 32 (d) 30
  27. 27.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 28 (b) 33 (c) 27 (d) 26
  28. 28.What is the 22nd term of the AP 10, 14, 18, 22, …? (a) 88 (b) 84 (c) 98 (d) 94
  29. 29.What is the missing term in the AP 12, ?, 30, 39, 48? (a) 30 (b) 20 (c) 21 (d) 22
  30. 30.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 11 (b) 14 (c) 12 (d) 13
  31. 31.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 40 (b) 240 (c) 440 (d) 220
  32. 32.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 75 (b) 78 (c) 150 (d) 15
  33. 33.Which term of the AP 10, 17, 24, 31, … is 171? (a) 25th (b) 24th (c) 26th (d) 23rd
  34. 34.What is the 28th term of the AP 1, 9, 17, 25, …? (a) 217 (b) 225 (c) 216 (d) 224
  35. 35.What is the 30th term of the AP 4, 6, 8, 10, …? (a) 62 (b) 60 (c) 64 (d) 58
  36. 36.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 370 (b) 185 (c) 200 (d) 32
  37. 37.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 140 (b) 26 (c) 85 (d) 70
  38. 38.What is the 38th term of the AP 20, 25, 30, 35, …? (a) 205 (b) 190 (c) 210 (d) 185
  39. 39.Which term of the AP 1, 10, 19, 28, … is 289? (a) 35th (b) 32nd (c) 33rd (d) 34th
  40. 40.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 8 (b) 10 (c) 9 (d) 14

Answer key

  1. 91
  2. 36
  3. 10th
  4. 144
  5. 25
  6. 100
  7. 139
  8. 54
  9. 255
  10. 66
  11. 19th
  12. 1431
  13. 37
  14. 78
  15. 4950
  16. 125
  17. 171
  18. 22
  19. 18
  20. 21st
  21. 208
  22. 1891
  23. 576
  24. 99
  25. 418
  26. 47
  27. 27
  28. 94
  29. 21
  30. 12
  31. 220
  32. 75
  33. 24th
  34. 217
  35. 62
  36. 185
  37. 70
  38. 205
  39. 33rd
  40. 9

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