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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 938 · 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 all the whole numbers from 1 to 14? (a) 98 (b) 210 (c) 105 (d) 91
  2. 2.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 54 (b) 102 (c) 11 (d) 51
  3. 3.What is the 29th term of the AP 2, 10, 18, 26, …? (a) 234 (b) 226 (c) 224 (d) 232
  4. 4.What is the 11th term of the AP 12, 14, 16, 18, …? (a) 22 (b) 32 (c) 20 (d) 34
  5. 5.What is the missing term in the AP 20, 27, 34, ?, 48? (a) 42 (b) 41 (c) 48 (d) 40
  6. 6.Which term of the AP 12, 20, 28, 36, … is 220? (a) 28th (b) 29th (c) 26th (d) 27th
  7. 7.What is the 29th term of the AP 8, 17, 26, 35, …? (a) 261 (b) 252 (c) 269 (d) 260
  8. 8.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 4556 (c) 2278 (d) 2279
  9. 9.What is the 37th term of the AP 11, 20, 29, 38, …? (a) 344 (b) 335 (c) 324 (d) 333
  10. 10.What is the 21st term of the AP 12, 17, 22, 27, …? (a) 117 (b) 105 (c) 112 (d) 100
  11. 11.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 300 (d) 650
  12. 12.What is the 26th term of the AP 12, 15, 18, 21, …? (a) 90 (b) 87 (c) 75 (d) 78
  13. 13.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 947 (c) 1892 (d) 903
  14. 14.Which term of the AP 1, 8, 15, 22, … is 204? (a) 32nd (b) 31st (c) 29th (d) 30th
  15. 15.Which term of the AP 10, 16, 22, 28, … is 130? (a) 22nd (b) 21st (c) 23rd (d) 20th
  16. 16.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 132 (b) 16 (c) 72 (d) 66
  17. 17.What is the 22nd term of the AP 10, 12, 14, 16, …? (a) 52 (b) 44 (c) 42 (d) 54
  18. 18.What is the 28th term of the AP 1, 10, 19, 28, …? (a) 253 (b) 243 (c) 244 (d) 252
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 190 (c) 380 (d) 361
  20. 20.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  21. 21.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 136 (d) 154
  22. 22.What is the 10th term of the AP 8, 11, 14, 17, …? (a) 38 (b) 27 (c) 35 (d) 30
  23. 23.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 3782 (c) 1830 (d) 1891
  24. 24.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 6 (b) 7 (c) 9 (d) 8
  25. 25.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 378 (b) 37 (c) 207 (d) 189
  26. 26.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 100 (b) 190 (c) 95 (d) 29
  27. 27.What is the 39th term of the AP 20, 26, 32, 38, …? (a) 254 (b) 248 (c) 228 (d) 234
  28. 28.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 156 (d) 78
  29. 29.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 444 (b) 480 (c) 70 (d) 888
  30. 30.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 6 (b) 7 (c) 9 (d) 5
  31. 31.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 26 (b) 23 (c) 22 (d) 21
  32. 32.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 230 (b) 115 (c) 16 (d) 120
  33. 33.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 300 (b) 156 (c) 18 (d) 150
  34. 34.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 195 (b) 390 (c) 33 (d) 210
  35. 35.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 17 (b) 81 (c) 162 (d) 90
  36. 36.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 153 (b) 144 (c) 24 (d) 288
  37. 37.What is the 18th term of the AP 14, 22, 30, 38, …? (a) 158 (b) 136 (c) 150 (d) 144
  38. 38.What is the 17th term of the AP 5, 9, 13, 17, …? (a) 64 (b) 68 (c) 73 (d) 69
  39. 39.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 34 (b) 180 (c) 324 (d) 162
  40. 40.What is the 16th term of the AP 4, 7, 10, 13, …? (a) 52 (b) 48 (c) 45 (d) 49

Answer key

  1. 105
  2. 51
  3. 226
  4. 32
  5. 41
  6. 27th
  7. 260
  8. 2278
  9. 335
  10. 112
  11. 325
  12. 87
  13. 946
  14. 30th
  15. 21st
  16. 66
  17. 52
  18. 244
  19. 361
  20. 400
  21. 153
  22. 35
  23. 1891
  24. 7
  25. 189
  26. 95
  27. 248
  28. 144
  29. 444
  30. 6
  31. 22
  32. 115
  33. 150
  34. 195
  35. 81
  36. 144
  37. 150
  38. 69
  39. 162
  40. 49

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