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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 347 · 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 359? (a) 42nd (b) 39th (c) 40th (d) 41st
  2. 2.Which term of the AP 2, 7, 12, 17, … is 122? (a) 24th (b) 25th (c) 26th (d) 27th
  3. 3.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  4. 4.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 42 (c) 36 (d) 72
  5. 5.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 29 (b) 133 (c) 119 (d) 238
  6. 6.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4851 (c) 9702 (d) 4753
  7. 7.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 66 (c) 78 (d) 72
  8. 8.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 286 (b) 572 (c) 46 (d) 308
  9. 9.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 2628 (c) 2701 (d) 5402
  10. 10.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 13 (b) 12 (c) 22 (d) 14
  11. 11.What is the 14th term of the AP 14, 20, 26, 32, …? (a) 98 (b) 78 (c) 84 (d) 92
  12. 12.What is the 13th term of the AP 17, 19, 21, 23, …? (a) 26 (b) 24 (c) 41 (d) 43
  13. 13.What is the 40th term of the AP 12, 18, 24, 30, …? (a) 240 (b) 234 (c) 252 (d) 246
  14. 14.What is the 22nd term of the AP 7, 13, 19, 25, …? (a) 133 (b) 126 (c) 139 (d) 132
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
  16. 16.What is the 13th term of the AP 12, 15, 18, 21, …? (a) 39 (b) 36 (c) 48 (d) 51
  17. 17.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 160 (b) 290 (c) 145 (d) 28
  18. 18.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 900 (d) 465
  19. 19.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 7832 (d) 3916
  20. 20.What is the 31st term of the AP 10, 13, 16, 19, …? (a) 100 (b) 90 (c) 93 (d) 103
  21. 21.What is the missing term in the AP 18, 24, 30, ?, 42? (a) 42 (b) 37 (c) 36 (d) 35
  22. 22.What is the 35th term of the AP 14, 23, 32, 41, …? (a) 329 (b) 306 (c) 320 (d) 315
  23. 23.Which term of the AP 2, 10, 18, 26, … is 146? (a) 20th (b) 19th (c) 21st (d) 18th
  24. 24.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 63 (b) 66 (c) 13 (d) 126
  25. 25.What is the 15th term of the AP 20, 27, 34, 41, …? (a) 125 (b) 98 (c) 105 (d) 118
  26. 26.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 43 (b) 506 (c) 253 (d) 275
  27. 27.What is the 32nd term of the AP 1, 3, 5, 7, …? (a) 64 (b) 65 (c) 63 (d) 62
  28. 28.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 176 (b) 179 (c) 31 (d) 352
  29. 29.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 18 (b) 25 (c) 19 (d) 17
  30. 30.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4754 (c) 4753 (d) 9506
  31. 31.What is the 16th term of the AP 5, 11, 17, 23, …? (a) 101 (b) 96 (c) 95 (d) 90
  32. 32.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 288 (b) 156 (c) 144 (d) 23
  33. 33.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 128 (c) 272 (d) 136
  34. 34.Which term of the AP 14, 21, 28, 35, … is 273? (a) 40th (b) 39th (c) 38th (d) 37th
  35. 35.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 5550 (c) 2738 (d) 2775
  36. 36.What is the 15th term of the AP 19, 25, 31, 37, …? (a) 84 (b) 90 (c) 109 (d) 103
  37. 37.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 288 (c) 276 (d) 300
  38. 38.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 12 (c) 51 (d) 50
  39. 39.Which term of the AP 20, 26, 32, 38, … is 122? (a) 20th (b) 18th (c) 19th (d) 17th
  40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 33 (d) 289

Answer key

  1. 40th
  2. 25th
  3. 25
  4. 36
  5. 119
  6. 4851
  7. 78
  8. 286
  9. 2701
  10. 13
  11. 92
  12. 41
  13. 246
  14. 133
  15. 400
  16. 48
  17. 145
  18. 900
  19. 3916
  20. 100
  21. 36
  22. 320
  23. 19th
  24. 63
  25. 118
  26. 253
  27. 63
  28. 176
  29. 18
  30. 4753
  31. 95
  32. 144
  33. 136
  34. 38th
  35. 2775
  36. 103
  37. 300
  38. 50
  39. 18th
  40. 289

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