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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 636 · 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 sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 35 (c) 11 (d) 40
  2. 2.Which term of the AP 8, 11, 14, 17, … is 71? (a) 23rd (b) 24th (c) 22nd (d) 21st
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 27 (d) 210
  4. 4.What is the 28th term of the AP 10, 15, 20, 25, …? (a) 135 (b) 150 (c) 145 (d) 140
  5. 5.What is the 32nd term of the AP 9, 11, 13, 15, …? (a) 62 (b) 71 (c) 64 (d) 73
  6. 6.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 2256 (c) 1081 (d) 1128
  7. 7.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 2070 (c) 1036 (d) 1035
  8. 8.Which term of the AP 20, 27, 34, 41, … is 216? (a) 28th (b) 30th (c) 31st (d) 29th
  9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 49 (d) 325
  10. 10.What is the 37th term of the AP 4, 12, 20, 28, …? (a) 288 (b) 296 (c) 300 (d) 292
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 576 (c) 600 (d) 47
  12. 12.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  13. 13.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 32 (b) 200 (c) 370 (d) 185
  14. 14.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 6642 (c) 3322 (d) 3321
  15. 15.Which term of the AP 10, 13, 16, 19, … is 91? (a) 27th (b) 28th (c) 30th (d) 29th
  16. 16.What is the 12th term of the AP 20, 25, 30, 35, …? (a) 60 (b) 55 (c) 80 (d) 75
  17. 17.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 252 (b) 126 (c) 26 (d) 129
  18. 18.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  19. 19.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 756 (d) 351
  20. 20.Which term of the AP 10, 13, 16, 19, … is 79? (a) 25th (b) 26th (c) 23rd (d) 24th
  21. 21.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 96 (b) 192 (c) 19 (d) 104
  22. 22.What is the 21st term of the AP 17, 26, 35, 44, …? (a) 189 (b) 180 (c) 206 (d) 197
  23. 23.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 240 (c) 121 (d) 120
  24. 24.What is the 16th term of the AP 2, 8, 14, 20, …? (a) 98 (b) 96 (c) 90 (d) 92
  25. 25.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 17 (b) 80 (c) 88 (d) 160
  26. 26.Which term of the AP 12, 18, 24, 30, … is 90? (a) 14th (b) 16th (c) 13th (d) 15th
  27. 27.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 32 (b) 33 (c) 41 (d) 34
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 28 (d) 13
  29. 29.What is the 33rd term of the AP 5, 8, 11, 14, …? (a) 101 (b) 99 (c) 96 (d) 104
  30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
  31. 31.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 19 (b) 22 (c) 18 (d) 20
  32. 32.What is the 35th term of the AP 15, 19, 23, 27, …? (a) 151 (b) 140 (c) 136 (d) 155
  33. 33.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 812 (c) 392 (d) 406
  34. 34.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 270 (b) 39 (c) 540 (d) 288
  35. 35.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 126 (b) 228 (c) 114 (d) 29
  36. 36.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 43 (c) 80 (d) 40
  37. 37.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 63 (b) 126 (c) 11 (d) 64
  38. 38.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 16 (b) 22 (c) 15 (d) 14
  39. 39.Which term of the AP 1, 4, 7, 10, … is 31? (a) 12th (b) 10th (c) 13th (d) 11th
  40. 40.What is the 22nd term of the AP 10, 17, 24, 31, …? (a) 164 (b) 147 (c) 154 (d) 157

Answer key

  1. 35
  2. 22nd
  3. 196
  4. 145
  5. 71
  6. 1128
  7. 1035
  8. 29th
  9. 625
  10. 292
  11. 576
  12. 441
  13. 185
  14. 3321
  15. 28th
  16. 75
  17. 126
  18. 100
  19. 378
  20. 24th
  21. 96
  22. 197
  23. 120
  24. 92
  25. 80
  26. 14th
  27. 33
  28. 49
  29. 101
  30. 64
  31. 19
  32. 151
  33. 406
  34. 270
  35. 114
  36. 40
  37. 63
  38. 15
  39. 11th
  40. 157

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