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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 229 · 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 9 terms of the AP 2, 4, 6, …? (a) 18 (b) 99 (c) 180 (d) 90
  2. 2.What is the 22nd term of the AP 15, 20, 25, 30, …? (a) 105 (b) 125 (c) 110 (d) 120
  3. 3.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 32 (b) 33 (c) 34 (d) 41
  4. 4.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 17 (b) 16 (c) 15 (d) 14
  5. 5.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 108 (c) 54 (d) 14
  6. 6.What is the 16th term of the AP 19, 25, 31, 37, …? (a) 90 (b) 96 (c) 109 (d) 115
  7. 7.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 119 (b) 224 (c) 112 (d) 22
  8. 8.Which term of the AP 7, 16, 25, 34, … is 79? (a) 8th (b) 9th (c) 10th (d) 11th
  9. 9.Which term of the AP 17, 23, 29, 35, … is 191? (a) 32nd (b) 30th (c) 29th (d) 31st
  10. 10.Which term of the AP 10, 12, 14, 16, … is 64? (a) 27th (b) 29th (c) 28th (d) 32nd
  11. 11.What is the sum of all the whole numbers from 1 to 76? (a) 2926 (b) 5852 (c) 2850 (d) 2888
  12. 12.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  13. 13.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 40 (c) 11 (d) 35
  14. 14.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 19 (b) 18 (c) 17 (d) 25
  15. 15.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 105 (b) 30 (c) 90 (d) 180
  16. 16.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 136 (c) 120 (d) 272
  17. 17.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 947 (c) 1892 (d) 946
  18. 18.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 27 (b) 54 (c) 7 (d) 30
  19. 19.What is the 30th term of the AP 14, 16, 18, 20, …? (a) 60 (b) 58 (c) 74 (d) 72
  20. 20.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
  21. 21.What is the 39th term of the AP 9, 16, 23, 30, …? (a) 273 (b) 282 (c) 275 (d) 266
  22. 22.What is the 37th term of the AP 2, 4, 6, 8, …? (a) 75 (b) 76 (c) 74 (d) 72
  23. 23.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2279 (c) 2278 (d) 2211
  24. 24.What is the 35th term of the AP 3, 9, 15, 21, …? (a) 213 (b) 204 (c) 210 (d) 207
  25. 25.What is the 24th term of the AP 13, 15, 17, 19, …? (a) 46 (b) 59 (c) 48 (d) 61
  26. 26.What is the 12th term of the AP 1, 6, 11, 16, …? (a) 56 (b) 61 (c) 55 (d) 60
  27. 27.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 576 (b) 288 (c) 312 (d) 46
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 435 (d) 841
  29. 29.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 2016 (d) 1953
  30. 30.Which term of the AP 11, 18, 25, 32, … is 109? (a) 17th (b) 14th (c) 15th (d) 16th
  31. 31.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 578 (c) 561 (d) 595
  32. 32.What is the 18th term of the AP 9, 12, 15, 18, …? (a) 63 (b) 60 (c) 51 (d) 54
  33. 33.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 20 (b) 154 (c) 80 (d) 77
  34. 34.Which term of the AP 8, 13, 18, 23, … is 163? (a) 34th (b) 32nd (c) 33rd (d) 31st
  35. 35.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 32 (b) 26 (c) 25 (d) 24
  36. 36.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 253 (d) 506
  37. 37.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 98 (b) 56 (c) 13 (d) 49
  38. 38.What is the 29th term of the AP 7, 9, 11, 13, …? (a) 58 (b) 56 (c) 65 (d) 63
  39. 39.What is the 33rd term of the AP 6, 14, 22, 30, …? (a) 270 (b) 256 (c) 264 (d) 262
  40. 40.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 20 (b) 104 (c) 112 (d) 208

Answer key

  1. 90
  2. 120
  3. 33
  4. 15
  5. 54
  6. 109
  7. 112
  8. 9th
  9. 30th
  10. 28th
  11. 2926
  12. 196
  13. 35
  14. 18
  15. 90
  16. 136
  17. 946
  18. 27
  19. 72
  20. 36
  21. 275
  22. 74
  23. 2278
  24. 207
  25. 59
  26. 56
  27. 288
  28. 841
  29. 2016
  30. 15th
  31. 595
  32. 60
  33. 77
  34. 32nd
  35. 25
  36. 484
  37. 49
  38. 63
  39. 262
  40. 104

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