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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 927 · 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 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
  2. 2.What is the 26th term of the AP 12, 21, 30, 39, …? (a) 225 (b) 246 (c) 234 (d) 237
  3. 3.What is the 33rd term of the AP 16, 18, 20, 22, …? (a) 66 (b) 82 (c) 64 (d) 80
  4. 4.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 78 (b) 132 (c) 66 (d) 21
  5. 5.Which term of the AP 17, 22, 27, 32, … is 147? (a) 26th (b) 27th (c) 28th (d) 29th
  6. 6.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 682 (c) 56 (d) 341
  7. 7.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 19 (b) 15 (c) 16 (d) 17
  8. 8.What is the missing term in the AP 12, 16, 20, ?, 28? (a) 28 (b) 25 (c) 24 (d) 23
  9. 9.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 55 (c) 110 (d) 50
  10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 9 (d) 15
  11. 11.Which term of the AP 4, 7, 10, 13, … is 49? (a) 16th (b) 17th (c) 15th (d) 18th
  12. 12.Which term of the AP 15, 22, 29, 36, … is 162? (a) 23rd (b) 24th (c) 22nd (d) 21st
  13. 13.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 280 (b) 560 (c) 310 (d) 55
  14. 14.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 34 (b) 220 (c) 125 (d) 110
  15. 15.What is the 16th term of the AP 20, 24, 28, 32, …? (a) 60 (b) 84 (c) 64 (d) 80
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 21 (d) 66
  17. 17.What is the 38th term of the AP 1, 3, 5, 7, …? (a) 74 (b) 77 (c) 76 (d) 75
  18. 18.Which term of the AP 16, 24, 32, 40, … is 312? (a) 37th (b) 40th (c) 39th (d) 38th
  19. 19.What is the 32nd term of the AP 4, 10, 16, 22, …? (a) 190 (b) 192 (c) 196 (d) 186
  20. 20.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 150 (b) 160 (c) 300 (d) 24
  21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 253 (d) 43
  22. 22.What is the 25th term of the AP 20, 22, 24, 26, …? (a) 48 (b) 50 (c) 70 (d) 68
  23. 23.What is the 20th term of the AP 20, 29, 38, 47, …? (a) 191 (b) 171 (c) 180 (d) 200
  24. 24.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 21 (b) 19 (c) 20 (d) 23
  25. 25.What is the 37th term of the AP 3, 7, 11, 15, …? (a) 144 (b) 151 (c) 148 (d) 147
  26. 26.What is the 13th term of the AP 13, 18, 23, 28, …? (a) 78 (b) 60 (c) 65 (d) 73
  27. 27.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 75 (b) 150 (c) 23 (d) 85
  28. 28.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 7 (b) 9 (c) 8 (d) 15
  29. 29.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 450 (c) 465 (d) 930
  30. 30.What is the 11th term of the AP 2, 11, 20, 29, …? (a) 101 (b) 99 (c) 90 (d) 92
  31. 31.What is the 27th term of the AP 11, 13, 15, 17, …? (a) 65 (b) 54 (c) 52 (d) 63
  32. 32.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 4 (b) 6 (c) 5 (d) 7
  33. 33.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 210 (d) 105
  34. 34.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 490 (b) 270 (c) 245 (d) 47
  35. 35.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 132 (c) 264 (d) 133
  36. 36.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4005 (c) 4095 (d) 4050
  37. 37.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 66 (c) 72 (d) 78
  38. 38.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2016 (c) 2048 (d) 4160
  39. 39.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 903 (c) 882 (d) 1806
  40. 40.What is the 27th term of the AP 4, 12, 20, 28, …? (a) 212 (b) 208 (c) 216 (d) 220

Answer key

  1. 81
  2. 237
  3. 80
  4. 66
  5. 27th
  6. 341
  7. 16
  8. 24
  9. 55
  10. 25
  11. 16th
  12. 22nd
  13. 280
  14. 110
  15. 80
  16. 121
  17. 75
  18. 38th
  19. 190
  20. 150
  21. 484
  22. 68
  23. 191
  24. 20
  25. 147
  26. 73
  27. 75
  28. 8
  29. 465
  30. 92
  31. 63
  32. 5
  33. 196
  34. 245
  35. 132
  36. 4095
  37. 78
  38. 2080
  39. 903
  40. 212

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