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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 921 · 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.Which term of the AP 18, 24, 30, 36, … is 168? (a) 25th (b) 26th (c) 28th (d) 27th
  2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 49 (d) 325
  3. 3.Which term of the AP 6, 13, 20, 27, … is 153? (a) 23rd (b) 21st (c) 22nd (d) 24th
  4. 4.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 20 (b) 21 (c) 27 (d) 19
  5. 5.What is the 37th term of the AP 1, 9, 17, 25, …? (a) 289 (b) 296 (c) 288 (d) 297
  6. 6.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 26 (b) 27 (c) 28 (d) 34
  7. 7.What is the 14th term of the AP 5, 10, 15, 20, …? (a) 70 (b) 71 (c) 75 (d) 65
  8. 8.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 23 (b) 22 (c) 21 (d) 24
  9. 9.What is the 33rd term of the AP 5, 13, 21, 29, …? (a) 269 (b) 264 (c) 256 (d) 261
  10. 10.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 29 (b) 27 (c) 37 (d) 28
  11. 11.What is the 15th term of the AP 20, 29, 38, 47, …? (a) 126 (b) 146 (c) 155 (d) 135
  12. 12.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 242 (c) 506 (d) 253
  13. 13.Which term of the AP 10, 16, 22, 28, … is 118? (a) 18th (b) 21st (c) 19th (d) 20th
  14. 14.What is the sum of all the whole numbers from 1 to 73? (a) 2702 (b) 2701 (c) 2628 (d) 5402
  15. 15.What is the 32nd term of the AP 3, 9, 15, 21, …? (a) 186 (b) 189 (c) 192 (d) 195
  16. 16.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 90 (b) 168 (c) 19 (d) 84
  17. 17.Which term of the AP 6, 9, 12, 15, … is 90? (a) 28th (b) 29th (c) 30th (d) 31st
  18. 18.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 51 (b) 696 (c) 372 (d) 348
  19. 19.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 210 (c) 105 (d) 91
  20. 20.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 31 (b) 32 (c) 30 (d) 40
  21. 21.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 45 (b) 90 (c) 46 (d) 11
  22. 22.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
  23. 23.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
  24. 24.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 297 (b) 594 (c) 302 (d) 52
  25. 25.What is the 26th term of the AP 4, 6, 8, 10, …? (a) 52 (b) 50 (c) 54 (d) 56
  26. 26.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 756 (d) 378
  27. 27.What is the 20th term of the AP 1, 8, 15, 22, …? (a) 134 (b) 141 (c) 140 (d) 133
  28. 28.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  29. 29.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  30. 30.What is the 10th term of the AP 5, 10, 15, 20, …? (a) 51 (b) 55 (c) 45 (d) 50
  31. 31.Which term of the AP 15, 18, 21, 24, … is 96? (a) 32nd (b) 29th (c) 27th (d) 28th
  32. 32.What is the 36th term of the AP 18, 20, 22, 24, …? (a) 88 (b) 70 (c) 90 (d) 72
  33. 33.What is the 38th term of the AP 12, 16, 20, 24, …? (a) 164 (b) 160 (c) 148 (d) 152
  34. 34.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 300 (c) 288 (d) 276
  35. 35.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 105 (b) 90 (c) 180 (d) 30
  36. 36.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 1806 (c) 903 (d) 861
  37. 37.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 143 (c) 286 (d) 18
  38. 38.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 384 (b) 54 (c) 768 (d) 408
  39. 39.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 23 (b) 21 (c) 22 (d) 28
  40. 40.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 231 (b) 220 (c) 30 (d) 440

Answer key

  1. 26th
  2. 625
  3. 22nd
  4. 20
  5. 289
  6. 27
  7. 70
  8. 22
  9. 261
  10. 28
  11. 146
  12. 253
  13. 19th
  14. 2701
  15. 189
  16. 84
  17. 29th
  18. 348
  19. 105
  20. 31
  21. 45
  22. 49
  23. 289
  24. 297
  25. 54
  26. 378
  27. 134
  28. 196
  29. 25
  30. 50
  31. 28th
  32. 88
  33. 160
  34. 300
  35. 90
  36. 903
  37. 143
  38. 384
  39. 22
  40. 220

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