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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 267 · 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 11, 18, 25, 32, … is 165? (a) 24th (b) 22nd (c) 25th (d) 23rd
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 153 (d) 289
  3. 3.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 18 (b) 17 (c) 19 (d) 16
  4. 4.Which term of the AP 20, 23, 26, 29, … is 56? (a) 13th (b) 12th (c) 15th (d) 14th
  5. 5.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 1892 (c) 946 (d) 947
  6. 6.What is the missing term in the AP 15, ?, 21, 24, 27? (a) 17 (b) 19 (c) 21 (d) 18
  7. 7.Which term of the AP 15, 18, 21, 24, … is 81? (a) 22nd (b) 23rd (c) 24th (d) 27th
  8. 8.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 435 (c) 870 (d) 436
  9. 9.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 21 (b) 15 (c) 14 (d) 16
  10. 10.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 59 (b) 374 (c) 748 (d) 379
  11. 11.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 69 (c) 429 (d) 462
  12. 12.What is the 24th term of the AP 11, 19, 27, 35, …? (a) 195 (b) 192 (c) 203 (d) 184
  13. 13.What is the 39th term of the AP 14, 17, 20, 23, …? (a) 117 (b) 128 (c) 131 (d) 114
  14. 14.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 480 (b) 252 (c) 31 (d) 240
  15. 15.Which term of the AP 3, 12, 21, 30, … is 120? (a) 14th (b) 13th (c) 16th (d) 15th
  16. 16.What is the 40th term of the AP 8, 10, 12, 14, …? (a) 88 (b) 86 (c) 80 (d) 78
  17. 17.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 26 (b) 18 (c) 17 (d) 19
  18. 18.What is the 38th term of the AP 5, 9, 13, 17, …? (a) 152 (b) 157 (c) 148 (d) 153
  19. 19.Which term of the AP 2, 4, 6, 8, … is 40? (a) 21st (b) 20th (c) 22nd (d) 19th
  20. 20.What is the 11th term of the AP 15, 23, 31, 39, …? (a) 95 (b) 88 (c) 80 (d) 103
  21. 21.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 630 (c) 1332 (d) 648
  22. 22.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 15 (b) 14 (c) 17 (d) 13
  23. 23.Which term of the AP 10, 19, 28, 37, … is 361? (a) 41st (b) 42nd (c) 40th (d) 39th
  24. 24.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 380 (b) 62 (c) 700 (d) 350
  25. 25.What is the 12th term of the AP 6, 11, 16, 21, …? (a) 66 (b) 61 (c) 60 (d) 55
  26. 26.Which term of the AP 4, 10, 16, 22, … is 154? (a) 26th (b) 27th (c) 28th (d) 25th
  27. 27.Which term of the AP 7, 16, 25, 34, … is 295? (a) 33rd (b) 34th (c) 32nd (d) 35th
  28. 28.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 72 (b) 144 (c) 16 (d) 80
  29. 29.Which term of the AP 3, 9, 15, 21, … is 183? (a) 31st (b) 30th (c) 32nd (d) 33rd
  30. 30.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 48 (b) 432 (c) 216 (d) 240
  31. 31.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3042 (c) 6162 (d) 3003
  32. 32.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 22 (b) 83 (c) 80 (d) 160
  33. 33.What is the sum of all the whole numbers from 1 to 27? (a) 756 (b) 379 (c) 351 (d) 378
  34. 34.What is the 16th term of the AP 2, 7, 12, 17, …? (a) 77 (b) 75 (c) 80 (d) 82
  35. 35.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 35 (b) 30 (c) 29 (d) 31
  36. 36.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 2352 (c) 1176 (d) 1128
  37. 37.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2450 (d) 2485
  38. 38.What is the 30th term of the AP 6, 15, 24, 33, …? (a) 276 (b) 267 (c) 261 (d) 270
  39. 39.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3486 (c) 3570 (d) 7140
  40. 40.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4465 (c) 4560 (d) 9120

Answer key

  1. 23rd
  2. 289
  3. 17
  4. 13th
  5. 946
  6. 18
  7. 23rd
  8. 435
  9. 15
  10. 374
  11. 429
  12. 195
  13. 128
  14. 240
  15. 14th
  16. 86
  17. 18
  18. 153
  19. 20th
  20. 95
  21. 666
  22. 14
  23. 40th
  24. 350
  25. 61
  26. 26th
  27. 33rd
  28. 72
  29. 31st
  30. 216
  31. 3081
  32. 80
  33. 378
  34. 77
  35. 30
  36. 1176
  37. 2485
  38. 267
  39. 3570
  40. 4560

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