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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 972 · 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 27th term of the AP 1, 6, 11, 16, …? (a) 130 (b) 135 (c) 131 (d) 136
  2. 2.What is the 16th term of the AP 8, 16, 24, 32, …? (a) 128 (b) 120 (c) 129 (d) 136
  3. 3.What is the 17th term of the AP 7, 10, 13, 16, …? (a) 48 (b) 51 (c) 55 (d) 58
  4. 4.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 55 (d) 110
  5. 5.Which term of the AP 18, 20, 22, 24, … is 36? (a) 18th (b) 11th (c) 9th (d) 10th
  6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  7. 7.Which term of the AP 7, 9, 11, 13, … is 77? (a) 38th (b) 35th (c) 36th (d) 37th
  8. 8.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 7140 (c) 3570 (d) 3528
  9. 9.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 308 (b) 53 (c) 616 (d) 313
  10. 10.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  11. 11.What is the missing term in the AP 11, 19, ?, 35, 43? (a) 27 (b) 28 (c) 26 (d) 35
  12. 12.Which term of the AP 19, 27, 35, 43, … is 171? (a) 20th (b) 22nd (c) 21st (d) 19th
  13. 13.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 496 (c) 465 (d) 992
  14. 14.What is the 27th term of the AP 10, 18, 26, 34, …? (a) 208 (b) 218 (c) 216 (d) 226
  15. 15.What is the 15th term of the AP 3, 12, 21, 30, …? (a) 135 (b) 126 (c) 138 (d) 129
  16. 16.What is the 35th term of the AP 7, 15, 23, 31, …? (a) 287 (b) 280 (c) 272 (d) 279
  17. 17.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1225 (c) 1176 (d) 1226
  18. 18.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 10 (b) 9 (c) 11 (d) 8
  19. 19.What is the 14th term of the AP 4, 13, 22, 31, …? (a) 117 (b) 126 (c) 130 (d) 121
  20. 20.What is the 21st term of the AP 19, 24, 29, 34, …? (a) 100 (b) 119 (c) 124 (d) 105
  21. 21.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  22. 22.What is the 21st term of the AP 5, 8, 11, 14, …? (a) 63 (b) 65 (c) 68 (d) 60
  23. 23.What is the 18th term of the AP 10, 12, 14, 16, …? (a) 46 (b) 36 (c) 34 (d) 44
  24. 24.What is the 34th term of the AP 9, 11, 13, 15, …? (a) 66 (b) 68 (c) 75 (d) 77
  25. 25.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 84 (b) 100 (c) 104 (d) 88
  26. 26.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 22 (b) 87 (c) 174 (d) 96
  27. 27.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 24 (b) 108 (c) 216 (d) 120
  28. 28.Which term of the AP 4, 13, 22, 31, … is 346? (a) 39th (b) 40th (c) 38th (d) 41st
  29. 29.What is the 23rd term of the AP 18, 24, 30, 36, …? (a) 150 (b) 132 (c) 156 (d) 138
  30. 30.Which term of the AP 18, 25, 32, 39, … is 74? (a) 11th (b) 8th (c) 9th (d) 10th
  31. 31.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 20 (b) 13 (c) 11 (d) 12
  32. 32.Which term of the AP 13, 18, 23, 28, … is 73? (a) 12th (b) 14th (c) 13th (d) 15th
  33. 33.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 95 (c) 80 (d) 160
  34. 34.What is the 16th term of the AP 17, 19, 21, 23, …? (a) 30 (b) 49 (c) 32 (d) 47
  35. 35.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 277 (c) 253 (d) 276
  36. 36.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 24 (b) 23 (c) 26 (d) 22
  37. 37.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 50 (b) 26 (c) 7 (d) 25
  38. 38.Which term of the AP 7, 10, 13, 16, … is 115? (a) 37th (b) 38th (c) 36th (d) 39th
  39. 39.Which term of the AP 18, 23, 28, 33, … is 173? (a) 34th (b) 33rd (c) 31st (d) 32nd
  40. 40.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 120 (b) 112 (c) 224 (d) 21

Answer key

  1. 131
  2. 128
  3. 55
  4. 55
  5. 10th
  6. 121
  7. 36th
  8. 3570
  9. 308
  10. 576
  11. 27
  12. 20th
  13. 496
  14. 218
  15. 129
  16. 279
  17. 1225
  18. 9
  19. 121
  20. 119
  21. 406
  22. 65
  23. 44
  24. 75
  25. 100
  26. 87
  27. 108
  28. 39th
  29. 150
  30. 9th
  31. 12
  32. 13th
  33. 80
  34. 47
  35. 276
  36. 23
  37. 25
  38. 37th
  39. 32nd
  40. 112

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