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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 899 · 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 11 terms of the AP 5, 7, 9, …? (a) 330 (b) 176 (c) 165 (d) 25
  2. 2.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 16 (b) 11 (c) 12 (d) 13
  3. 3.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 288 (b) 39 (c) 270 (d) 540
  4. 4.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 136 (d) 272
  5. 5.What is the 39th term of the AP 5, 12, 19, 26, …? (a) 266 (b) 278 (c) 271 (d) 273
  6. 6.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 2256 (c) 1129 (d) 1081
  7. 7.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 4851 (d) 9900
  8. 8.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 436 (c) 406 (d) 870
  9. 9.What is the 14th term of the AP 4, 8, 12, 16, …? (a) 60 (b) 52 (c) 56 (d) 57
  10. 10.What is the 13th term of the AP 6, 15, 24, 33, …? (a) 117 (b) 108 (c) 123 (d) 114
  11. 11.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 4556 (c) 2279 (d) 2278
  12. 12.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 21 (b) 20 (c) 28 (d) 22
  13. 13.What is the 12th term of the AP 12, 14, 16, 18, …? (a) 22 (b) 36 (c) 34 (d) 24
  14. 14.Which term of the AP 7, 14, 21, 28, … is 70? (a) 11th (b) 10th (c) 9th (d) 12th
  15. 15.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 342 (b) 56 (c) 684 (d) 372
  16. 16.What is the 40th term of the AP 17, 25, 33, 41, …? (a) 312 (b) 329 (c) 320 (d) 337
  17. 17.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 26 (b) 33 (c) 25 (d) 24
  18. 18.What is the 24th term of the AP 1, 5, 9, 13, …? (a) 97 (b) 96 (c) 93 (d) 92
  19. 19.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 23 (b) 70 (c) 65 (d) 130
  20. 20.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 19 (b) 104 (c) 192 (d) 96
  21. 21.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 48 (b) 510 (c) 255 (d) 280
  22. 22.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 286 (b) 572 (c) 291 (d) 51
  23. 23.What is the 23rd term of the AP 4, 12, 20, 28, …? (a) 184 (b) 176 (c) 188 (d) 180
  24. 24.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 53 (b) 288 (c) 522 (d) 261
  25. 25.What is the 18th term of the AP 1, 8, 15, 22, …? (a) 119 (b) 120 (c) 126 (d) 127
  26. 26.What is the 38th term of the AP 8, 10, 12, 14, …? (a) 84 (b) 74 (c) 82 (d) 76
  27. 27.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 5 (b) 6 (c) 7 (d) 8
  28. 28.Which term of the AP 3, 12, 21, 30, … is 156? (a) 17th (b) 19th (c) 18th (d) 20th
  29. 29.Which term of the AP 11, 18, 25, 32, … is 270? (a) 37th (b) 39th (c) 40th (d) 38th
  30. 30.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 336 (b) 48 (c) 624 (d) 312
  31. 31.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  32. 32.What is the 12th term of the AP 10, 14, 18, 22, …? (a) 44 (b) 48 (c) 58 (d) 54
  33. 33.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 10 (b) 8 (c) 15 (d) 9
  34. 34.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 130 (c) 70 (d) 65
  35. 35.Which term of the AP 18, 20, 22, 24, … is 74? (a) 30th (b) 28th (c) 37th (d) 29th
  36. 36.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 8372 (c) 4187 (d) 4186
  37. 37.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1596 (c) 3192 (d) 1568
  38. 38.What is the 12th term of the AP 15, 17, 19, 21, …? (a) 22 (b) 39 (c) 24 (d) 37
  39. 39.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3916 (d) 3828
  40. 40.What is the missing term in the AP 18, 24, 30, ?, 42? (a) 37 (b) 35 (c) 36 (d) 42

Answer key

  1. 165
  2. 12
  3. 270
  4. 256
  5. 271
  6. 1128
  7. 4950
  8. 435
  9. 56
  10. 114
  11. 2278
  12. 21
  13. 34
  14. 10th
  15. 342
  16. 329
  17. 25
  18. 93
  19. 65
  20. 96
  21. 255
  22. 286
  23. 180
  24. 261
  25. 120
  26. 82
  27. 6
  28. 18th
  29. 38th
  30. 312
  31. 225
  32. 54
  33. 9
  34. 65
  35. 29th
  36. 4186
  37. 1596
  38. 37
  39. 3916
  40. 36

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