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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 974 · 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 22nd term of the AP 16, 18, 20, 22, …? (a) 42 (b) 58 (c) 44 (d) 60
  2. 2.What is the 19th term of the AP 14, 16, 18, 20, …? (a) 52 (b) 50 (c) 36 (d) 38
  3. 3.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 1596 (c) 1653 (d) 3306
  4. 4.What is the 38th term of the AP 2, 9, 16, 23, …? (a) 259 (b) 266 (c) 268 (d) 261
  5. 5.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 168 (b) 184 (c) 336 (d) 35
  6. 6.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 210 (b) 378 (c) 189 (d) 45
  7. 7.What is the sum of the first 12 terms of the AP 9, 13, 17, …? (a) 396 (b) 53 (c) 372 (d) 744
  8. 8.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 338 (d) 702
  9. 9.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 9 (c) 50 (d) 25
  10. 10.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 22 (b) 13 (c) 14 (d) 15
  11. 11.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 5852 (c) 2850 (d) 2926
  12. 12.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 70 (b) 73 (c) 19 (d) 140
  13. 13.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 31 (b) 38 (c) 33 (d) 32
  14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  15. 15.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 484 (d) 506
  16. 16.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 168 (b) 14 (c) 88 (d) 84
  17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 33 (d) 153
  18. 18.What is the 25th term of the AP 6, 8, 10, 12, …? (a) 48 (b) 54 (c) 56 (d) 50
  19. 19.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 26 (c) 81 (d) 96
  20. 20.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 240 (b) 440 (c) 220 (d) 40
  21. 21.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 852 (b) 456 (c) 63 (d) 426
  22. 22.What is the 11th term of the AP 19, 24, 29, 34, …? (a) 74 (b) 55 (c) 69 (d) 50
  23. 23.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  24. 24.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 444 (c) 816 (d) 408
  25. 25.What is the 25th term of the AP 13, 20, 27, 34, …? (a) 188 (b) 175 (c) 181 (d) 168
  26. 26.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 3160 (c) 6320 (d) 3161
  27. 27.What is the sum of the first 11 terms of the AP 5, 10, 15, …? (a) 335 (b) 330 (c) 55 (d) 660
  28. 28.What is the 12th term of the AP 12, 19, 26, 33, …? (a) 96 (b) 77 (c) 84 (d) 89
  29. 29.Which term of the AP 17, 23, 29, 35, … is 197? (a) 33rd (b) 31st (c) 32nd (d) 30th
  30. 30.What is the sum of all the whole numbers from 1 to 53? (a) 1431 (b) 1378 (c) 2862 (d) 1432
  31. 31.What is the 14th term of the AP 2, 11, 20, 29, …? (a) 126 (b) 117 (c) 128 (d) 119
  32. 32.What is the 29th term of the AP 16, 19, 22, 25, …? (a) 103 (b) 87 (c) 84 (d) 100
  33. 33.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 176 (b) 352 (c) 31 (d) 179
  34. 34.Which term of the AP 1, 4, 7, 10, … is 37? (a) 15th (b) 13th (c) 12th (d) 14th
  35. 35.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 319 (b) 49 (c) 638 (d) 341
  36. 36.What is the 37th term of the AP 20, 28, 36, 44, …? (a) 296 (b) 288 (c) 316 (d) 308
  37. 37.What is the 22nd term of the AP 18, 27, 36, 45, …? (a) 216 (b) 189 (c) 207 (d) 198
  38. 38.What is the 17th term of the AP 2, 4, 6, 8, …? (a) 32 (b) 36 (c) 34 (d) 35
  39. 39.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 162 (b) 34 (c) 180 (d) 324
  40. 40.Which term of the AP 13, 20, 27, 34, … is 258? (a) 36th (b) 37th (c) 38th (d) 35th

Answer key

  1. 58
  2. 50
  3. 1653
  4. 261
  5. 168
  6. 189
  7. 372
  8. 351
  9. 25
  10. 14
  11. 2926
  12. 70
  13. 32
  14. 36
  15. 484
  16. 84
  17. 289
  18. 54
  19. 81
  20. 220
  21. 426
  22. 69
  23. 81
  24. 408
  25. 181
  26. 3160
  27. 330
  28. 89
  29. 31st
  30. 1431
  31. 119
  32. 100
  33. 176
  34. 13th
  35. 319
  36. 308
  37. 207
  38. 34
  39. 162
  40. 36th

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