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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 311 · 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 7 terms of the AP 4, 10, 16, …? (a) 40 (b) 308 (c) 175 (d) 154
  2. 2.What is the 21st term of the AP 18, 27, 36, 45, …? (a) 180 (b) 207 (c) 189 (d) 198
  3. 3.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 100 (d) 55
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 210 (d) 27
  5. 5.Which term of the AP 16, 19, 22, 25, … is 58? (a) 17th (b) 16th (c) 15th (d) 14th
  6. 6.What is the 24th term of the AP 7, 11, 15, 19, …? (a) 103 (b) 96 (c) 99 (d) 92
  7. 7.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1058 (c) 1035 (d) 1081
  8. 8.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 48 (b) 13 (c) 54 (d) 96
  9. 9.What is the missing term in the AP 17, 22, 27, ?, 37? (a) 32 (b) 33 (c) 37 (d) 31
  10. 10.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
  11. 11.Which term of the AP 11, 13, 15, 17, … is 25? (a) 10th (b) 7th (c) 8th (d) 9th
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  13. 13.What is the 19th term of the AP 2, 9, 16, 23, …? (a) 133 (b) 135 (c) 128 (d) 126
  14. 14.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 224 (b) 117 (c) 31 (d) 112
  15. 15.What is the 14th term of the AP 1, 3, 5, 7, …? (a) 26 (b) 29 (c) 27 (d) 28
  16. 16.What is the missing term in the AP 15, 23, 31, ?, 47? (a) 47 (b) 39 (c) 40 (d) 38
  17. 17.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2556 (c) 2592 (d) 2628
  18. 18.What is the 24th term of the AP 16, 20, 24, 28, …? (a) 108 (b) 96 (c) 92 (d) 112
  19. 19.What is the 38th term of the AP 11, 18, 25, 32, …? (a) 266 (b) 259 (c) 277 (d) 270
  20. 20.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 198 (b) 100 (c) 99 (d) 15
  21. 21.What is the 28th term of the AP 3, 7, 11, 15, …? (a) 108 (b) 112 (c) 111 (d) 115
  22. 22.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 135 (b) 144 (c) 270 (d) 23
  23. 23.Which term of the AP 2, 6, 10, 14, … is 114? (a) 29th (b) 30th (c) 31st (d) 28th
  24. 24.What is the 18th term of the AP 4, 9, 14, 19, …? (a) 90 (b) 85 (c) 94 (d) 89
  25. 25.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 13 (b) 14 (c) 12 (d) 18
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 256 (d) 136
  27. 27.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 630 (d) 648
  28. 28.Which term of the AP 12, 14, 16, 18, … is 70? (a) 35th (b) 29th (c) 31st (d) 30th
  29. 29.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 70 (b) 65 (c) 130 (d) 17
  30. 30.What is the missing term in the AP 10, ?, 28, 37, 46? (a) 19 (b) 18 (c) 20 (d) 28
  31. 31.What is the 27th term of the AP 8, 11, 14, 17, …? (a) 78 (b) 89 (c) 86 (d) 81
  32. 32.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 138 (c) 144 (d) 17
  33. 33.What is the 33rd term of the AP 1, 8, 15, 22, …? (a) 231 (b) 232 (c) 224 (d) 225
  34. 34.What is the 13th term of the AP 19, 21, 23, 25, …? (a) 45 (b) 26 (c) 43 (d) 24
  35. 35.What is the missing term in the AP 14, 19, ?, 29, 34? (a) 25 (b) 23 (c) 29 (d) 24
  36. 36.What is the missing term in the AP 5, 8, ?, 14, 17? (a) 12 (b) 14 (c) 10 (d) 11
  37. 37.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 49 (b) 341 (c) 638 (d) 319
  38. 38.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 216 (b) 432 (c) 48 (d) 240
  39. 39.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 240 (b) 29 (c) 136 (d) 120
  40. 40.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 49 (b) 225 (c) 450 (d) 252

Answer key

  1. 154
  2. 198
  3. 100
  4. 196
  5. 15th
  6. 99
  7. 1081
  8. 48
  9. 32
  10. 169
  11. 8th
  12. 729
  13. 128
  14. 112
  15. 27
  16. 39
  17. 2628
  18. 108
  19. 270
  20. 99
  21. 111
  22. 135
  23. 29th
  24. 89
  25. 13
  26. 256
  27. 666
  28. 30th
  29. 65
  30. 19
  31. 86
  32. 138
  33. 225
  34. 43
  35. 24
  36. 11
  37. 319
  38. 216
  39. 120
  40. 225

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