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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 378 · 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.Which term of the AP 8, 17, 26, 35, … is 278? (a) 33rd (b) 31st (c) 32nd (d) 30th
  2. 2.What is the 12th term of the AP 5, 13, 21, 29, …? (a) 101 (b) 88 (c) 93 (d) 96
  3. 3.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  4. 4.Which term of the AP 12, 20, 28, 36, … is 308? (a) 40th (b) 37th (c) 39th (d) 38th
  5. 5.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 290 (b) 45 (c) 540 (d) 270
  6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  7. 7.What is the 37th term of the AP 5, 10, 15, 20, …? (a) 186 (b) 180 (c) 190 (d) 185
  8. 8.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  9. 9.Which term of the AP 14, 22, 30, 38, … is 302? (a) 38th (b) 37th (c) 39th (d) 36th
  10. 10.What is the 37th term of the AP 9, 14, 19, 24, …? (a) 180 (b) 194 (c) 189 (d) 185
  11. 11.Which term of the AP 3, 9, 15, 21, … is 147? (a) 24th (b) 25th (c) 27th (d) 26th
  12. 12.What is the 23rd term of the AP 4, 7, 10, 13, …? (a) 73 (b) 66 (c) 70 (d) 69
  13. 13.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  14. 14.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 36 (b) 38 (c) 37 (d) 46
  15. 15.What is the 15th term of the AP 4, 13, 22, 31, …? (a) 126 (b) 135 (c) 139 (d) 130
  16. 16.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 75 (b) 21 (c) 130 (d) 65
  17. 17.What is the 29th term of the AP 20, 28, 36, 44, …? (a) 232 (b) 252 (c) 244 (d) 224
  18. 18.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 180 (b) 162 (c) 324 (d) 34
  19. 19.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 24 (b) 33 (c) 25 (d) 26
  20. 20.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 135 (b) 270 (c) 27 (d) 138
  21. 21.What is the 36th term of the AP 6, 11, 16, 21, …? (a) 181 (b) 175 (c) 180 (d) 186
  22. 22.Which term of the AP 4, 6, 8, 10, … is 82? (a) 41st (b) 40th (c) 42nd (d) 39th
  23. 23.What is the 28th term of the AP 12, 18, 24, 30, …? (a) 162 (b) 168 (c) 180 (d) 174
  24. 24.Which term of the AP 17, 20, 23, 26, … is 47? (a) 13th (b) 11th (c) 10th (d) 12th
  25. 25.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 561 (c) 528 (d) 1122
  26. 26.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  27. 27.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 154 (b) 78 (c) 14 (d) 77
  28. 28.Which term of the AP 5, 13, 21, 29, … is 93? (a) 13th (b) 12th (c) 14th (d) 11th
  29. 29.What is the 13th term of the AP 9, 18, 27, 36, …? (a) 126 (b) 108 (c) 117 (d) 118
  30. 30.What is the 18th term of the AP 6, 8, 10, 12, …? (a) 36 (b) 42 (c) 40 (d) 34
  31. 31.Which term of the AP 9, 17, 25, 33, … is 289? (a) 38th (b) 37th (c) 36th (d) 35th
  32. 32.What is the 39th term of the AP 12, 14, 16, 18, …? (a) 76 (b) 88 (c) 90 (d) 78
  33. 33.What is the 28th term of the AP 8, 13, 18, 23, …? (a) 140 (b) 143 (c) 148 (d) 135
  34. 34.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3698 (c) 3741 (d) 7482
  35. 35.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 57 (c) 12 (d) 60
  36. 36.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 72 (b) 144 (c) 16 (d) 80
  37. 37.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 13 (b) 14 (c) 12 (d) 11
  38. 38.What is the 14th term of the AP 7, 10, 13, 16, …? (a) 46 (b) 42 (c) 49 (d) 39
  39. 39.What is the missing term in the AP 8, 15, 22, ?, 36? (a) 30 (b) 28 (c) 36 (d) 29
  40. 40.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 368 (b) 37 (c) 200 (d) 184

Answer key

  1. 31st
  2. 93
  3. 529
  4. 38th
  5. 270
  6. 144
  7. 185
  8. 121
  9. 37th
  10. 189
  11. 25th
  12. 70
  13. 576
  14. 37
  15. 130
  16. 65
  17. 244
  18. 162
  19. 25
  20. 135
  21. 181
  22. 40th
  23. 174
  24. 11th
  25. 561
  26. 81
  27. 77
  28. 12th
  29. 117
  30. 40
  31. 36th
  32. 88
  33. 143
  34. 3741
  35. 57
  36. 72
  37. 12
  38. 46
  39. 29
  40. 184

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